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RD Sharma solutions for Class 8 Mathematics chapter 3 - Squares and Square Roots

Mathematics for Class 8 by R D Sharma (2019-2020 Session)

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RD Sharma Mathematics Class 8 by R D Sharma (2019-2020 Session)

Mathematics for Class 8 by R D Sharma (2019-2020 Session) - Shaalaa.com

Chapter 3: Squares and Square Roots

Ex. 3.10Ex. 3.20Ex. 3.30Ex. 3.40Ex. 3.50Ex. 3.60Ex. 3.70Ex. 3.80Ex. 3.90

Chapter 3: Squares and Square Roots Exercise 3.10 solutions [Pages 4 - 5]

Ex. 3.10 | Q 1.1 | Page 4

Which of the following numbers are perfect squares?

484

Ex. 3.10 | Q 1.2 | Page 4

Which of the following numbers are perfect squares?

625 

Ex. 3.10 | Q 1.3 | Page 4

Which of the following numbers are perfect squares? 

576 

Ex. 3.10 | Q 1.4 | Page 4

Which of the following numbers are perfect squares? 

 941 

Ex. 3.10 | Q 1.5 | Page 4

Which of the following numbers are perfect squares? 

961 

Ex. 3.10 | Q 1.6 | Page 4

Which of the following numbers are perfect squares? 

 2500 

Ex. 3.10 | Q 2.1 | Page 4

Show that each of the following numbers is a perfect square. Also, find the number whose square is the given number in each case: 

1156 

Ex. 3.10 | Q 2.2 | Page 4

Show that each of the following numbers is a perfect square. Also, find the numer whose square is the given number in each case: 

2025 

Ex. 3.10 | Q 2.3 | Page 4

Show that each of the following numbers is a perfect square. Also, find the number whose square is the given number in each case:

 14641 

 

Ex. 3.10 | Q 2.4 | Page 4

Show that each of the following numbers is a perfect square. Also, find the number whose square is the given number in each case: 

 4761 

Ex. 3.10 | Q 3.1 | Page 4

Find the smallest number by which the given number must bew multiplied so that the product is a perfect square: 

 23805 

Ex. 3.10 | Q 3.2 | Page 4

Find the smallest number by which the given number must bew multiplied so that the product is a perfect square: 

12150 

Ex. 3.10 | Q 3.3 | Page 4

Find the smallest number by which the given number must bew multiplied so that the product is a perfect square: 

7688 

Ex. 3.10 | Q 4.1 | Page 4

Find the smallest number by which the given number must be divided so that the resulting number is a perfect square:

14283 

Ex. 3.10 | Q 4.2 | Page 4

Find the smallest number by which the given number must be divided so that the resulting number is a perfect square: 

1800 

 

Ex. 3.10 | Q 4.3 | Page 4

Find the smallest number by which the given number must be divided so that the resulting number is a perfect square: 

2904

Ex. 3.10 | Q 5.01 | Page 4

Which of the following numbers are perfect square?

11 

Ex. 3.10 | Q 5.02 | Page 4

Which of the following numbers are perfect square? 

12 

Ex. 3.10 | Q 5.03 | Page 4

Which of the following numbers are perfect square?  

16 

Ex. 3.10 | Q 5.04 | Page 4

Which of the following numbers are perfect square?

32 

Ex. 3.10 | Q 5.05 | Page 4

Which of the following numbers are perfect squares? 

 36 

Ex. 3.10 | Q 5.06 | Page 4

Which of the following numbers are perfect square? 

 50 

Ex. 3.10 | Q 5.07 | Page 4

Which of the following numbers are perfect square? 

 64 

Ex. 3.10 | Q 5.08 | Page 4

Which of the following numbers are perfect square? 

79 

Ex. 3.10 | Q 5.09 | Page 4

Which of the following numbers are perfect square? 

81 

Ex. 3.10 | Q 5.1 | Page 4

Which of the following numbers are perfect square? 

111

Ex. 3.10 | Q 5.11 | Page 4

Which of the following numbers are perfect square? 

121 

Ex. 3.10 | Q 6.1 | Page 4

Using prime factorization method, find which of the following numbers are perfect square? 

189, 

Ex. 3.10 | Q 6.2 | Page 4

Using prime factorization method, find which of the following numbers are perfect square?  

225 

Ex. 3.10 | Q 6.3 | Page 4

Using prime factorization method, find which of the following numbers are perfect square? 

2048 

Ex. 3.10 | Q 6.4 | Page 4

Using prime factorization method, find which of the following numbers are perfect square? 

343 

Ex. 3.10 | Q 6.5 | Page 4

Using prime factorization method, find which of the following numbers are perfect square? 

441

Ex. 3.10 | Q 6.6 | Page 4

Using prime factorization method, find which of the following numbers are perfect square? 

2916

Ex. 3.10 | Q 6.7 | Page 4

Using prime factorization method, find which of the following numbers are perfect square? 

11025

Ex. 3.10 | Q 6.8 | Page 4

Using prime factorization method, find which of the following numbers are perfect square? 

3549

Ex. 3.10 | Q 7.1 | Page 4

By what number should each of the following numbers be multiplied to get a perfect square ? Also, find the number whose square is the new number. 

8820

 

Ex. 3.10 | Q 7.2 | Page 4

By what number should each of the following numbers be multiplied to get a perfect square ? Also, find the number whose square is the new number. 

3675

Ex. 3.10 | Q 7.3 | Page 4

By what number should each of the following numbers be multiplied to get a perfect square? Also, find the number whose square is the new number. 

605 

Ex. 3.10 | Q 7.4 | Page 4

By what number should each of the following numbers be multiplied to get a perfect square? Also, find the number whose square is the new number. 

2880

Ex. 3.10 | Q 7.5 | Page 4

By what number should each of the following numbers be multiplied to get a perfect square? Also, find the number whose square is the new number.  

 4056

Ex. 3.10 | Q 7.6 | Page 4

By what number should each of the following numbers be multiplied to get a perfect square ? Also, find the number whose square is the new number. 

3468

Ex. 3.10 | Q 7.7 | Page 4

By what number should each of the following numbers be multiplied to get a perfect square ? Also, find the number whose square is the new number. 

7776 

Ex. 3.10 | Q 8.1 | Page 4

By what numbers should each of the following be divided to get a perfect square ? Also, find the number whose square is the new number. 

16562 

Ex. 3.10 | Q 8.2 | Page 4

By what numbers should each of the following be divided to get a perfect square? Also, find the number whose square is the new number. 

 3698

Ex. 3.10 | Q 8.3 | Page 4

By what numbers should each of the following be divided to get a perfect square ? Also, find the number whose square is the new number. 

 5103

Ex. 3.10 | Q 8.4 | Page 4

By what numbers should each of the following be divided to get a perfect square? Also, find the number whose square is the new number. 

 3174

Ex. 3.10 | Q 8.5 | Page 4

By what numbers should each of the following be divided to get a perfect square ? Also, find the number whose square is the new number. 

 1575 

Ex. 3.10 | Q 9 | Page 4

Find the greatest number of two digits which is a perfect square.

 

 

Ex. 3.10 | Q 10 | Page 4

Find the least number of three digits which is perfect square.

 

Ex. 3.10 | Q 11 | Page 5

Find the smallest number by which 4851 must be multiplied so that the product becomes a perfect suqare. 

 

Ex. 3.10 | Q 12 | Page 5

Find the smallest number by which 28812 must be divided so that the quotient becomes a perfect square. 

Ex. 3.10 | Q 13 | Page 5

Find the smallest number by which 1152 must be divided so that it becomes a perfect square. Also, find the number whose square is the resulting number.

Chapter 3: Squares and Square Roots Exercise 3.20 solutions [Pages 18 - 20]

Ex. 3.20 | Q 1.1 | Page 18

The following number are not perfect squares. Give reason. 

 1547

Ex. 3.20 | Q 1.2 | Page 18

The following number is  not perfect square. Give reason. 

45743

Ex. 3.20 | Q 1.3 | Page 18

The following number is not perfect square. Give reason.

8948

Ex. 3.20 | Q 1.4 | Page 18

The following number is not perfect square. Give reason. 

333333

Ex. 3.20 | Q 2.1 | Page 18

Show that the following number is not perfect square: 

 9327 

 

Ex. 3.20 | Q 2.2 | Page 18

Show that the following number is not perfect square:

4058 

Ex. 3.20 | Q 2.3 | Page 18

Show that the following number is not perfect square: 

22453 

Ex. 3.20 | Q 2.4 | Page 18

Show that the following number is not perfect square: 

 743522 

Ex. 3.20 | Q 3.1 | Page 18

The square of which of the following number would be an odd number? 

 731 

Ex. 3.20 | Q 3.2 | Page 18

The square of which of the following number would be an odd number? 

3456 

Ex. 3.20 | Q 3.3 | Page 18

The square of which of the following number would be an odd number? 

5559 

Ex. 3.20 | Q 3.4 | Page 18

The square of which of the following number would be an odd number? 

 42008 

Ex. 3.20 | Q 4.1 | Page 19

What will be the units digit of the square of the following number?

52

Ex. 3.20 | Q 4.2 | Page 19

What will be the units digit of the square of the following number? 

977 

Ex. 3.20 | Q 4.3 | Page 19

What will be the units digit of the square of the following number? 

 4583 

Ex. 3.20 | Q 4.4 | Page 19

What will be the units digit of the square of the following number? 

 78367 

Ex. 3.20 | Q 4.5 | Page 19

What will be the units digit of the square of the following number?  

52698 

Ex. 3.20 | Q 4.6 | Page 19

What will be the units digit of the square of the following number? 

 99880 

Ex. 3.20 | Q 4.7 | Page 19

What will be the units digit of the square of the following number? 

 12796

Ex. 3.20 | Q 4.8 | Page 19

What will be the units digit of the square of the following number? 

55555

Ex. 3.20 | Q 4.9 | Page 19

What will be the units digit of the square of the following number?

 53924

Ex. 3.20 | Q 5 | Page 19

From the pattern, we can say that the sum of the first n positive odd numbers is equal to the square of the n-th positive number. Putting that into formula:
1 + 3 + 5 + 7 + ...  n =  n2, where the left hand side consists of n terms. 

Ex. 3.20 | Q 6.1 | Page 19

Observe the following pattern 

22 − 12 = 2 + 1
32 − 22 = 3 + 2
42 − 32 = 4 + 3
52 − 42 = 5 + 4
and find the value of 

1002 − 992

Ex. 3.20 | Q 6.2 | Page 19

Observe the following pattern
22 − 12 = 2 + 1
32 − 22 = 3 + 2
42 − 32 = 4 + 3
52 − 42 = 5 + 4
and find the value of 

 1112 − 1092

Ex. 3.20 | Q 6.3 | Page 19

Observe the following pattern
22 − 12 = 2 + 1
32 − 22 = 3 + 2
42 − 32 = 4 + 3 
52 − 42 = 5 + 4
and find the value of 

992 − 962

Ex. 3.20 | Q 7.1 | Page 19

Which of the following triplets are pythagorean? 

 (8, 15, 17)

Ex. 3.20 | Q 7.2 | Page 19

Which of the following triplet is pythagorean? 

 (18, 80, 82) 

Ex. 3.20 | Q 7.3 | Page 19

Which of the following triplet  pythagorean? 

 (14, 48, 51)

Ex. 3.20 | Q 7.4 | Page 19

Which of the following triplet  pythagorean?  

(10, 24, 26)

Ex. 3.20 | Q 7.5 | Page 19

Which of the following triplet pythagorean? 

(16, 63, 65)

Ex. 3.20 | Q 7.6 | Page 19

Which of the following triplet  pythagorean? 

(12, 35, 38) 

Ex. 3.20 | Q 8 | Page 19

Observe the following pattern 

\[\left( 1 \times 2 \right) + \left( 2 \times 3 \right) = \frac{2 \times 3 \times 4}{3}\] 

\[\left( 1 \times 2 \right) + \left( 2 \times 3 \right) + \left( 3 \times 4 \right) = \frac{3 \times 4 \times 5}{3}\] 

\[\left( 1 \times 2 \right) + \left( 2 \times 3 \right) + \left( 3 \times 4 \right) + \left( 4 \times 5 \right) = \frac{4 \times 5 \times 6}{3}\] 

and find the value of(1 × 2) + (2 × 3) + (3 × 4) + (4 × 5) + (5 × 6)

Ex. 3.20 | Q 9.1 | Page 19

Observe the following pattern \[1 = \frac{1}{2}\left\{ 1 \times \left( 1 + 1 \right) \right\}\]
\[ 1 + 2 = \frac{1}{2}\left\{ 2 \times \left( 2 + 1 \right) \right\}\]
\[ 1 + 2 + 3 = \frac{1}{2}\left\{ 3 \times \left( 3 + 1 \right) \right\}\]
\[1 + 2 + 3 + 4 = \frac{1}{2}\left\{ 4 \times \left( 4 + 1 \right) \right\}\] 

and find the values of  following: 

1 + 2 + 3 + 4 + 5 + ... + 50

Ex. 3.20 | Q 9.2 | Page 19

Observe the following pattern \[1 = \frac{1}{2}\left\{ 1 \times \left( 1 + 1 \right) \right\}\]
\[ 1 + 2 = \frac{1}{2}\left\{ 2 \times \left( 2 + 1 \right) \right\}\]
\[ 1 + 2 + 3 = \frac{1}{2}\left\{ 3 \times \left( 3 + 1 \right) \right\}\]
\[1 + 2 + 3 + 4 = \frac{1}{2}\left\{ 4 \times \left( 4 + 1 \right) \right\}\]and find the values of following:

31 + 32 + ... + 50

Ex. 3.20 | Q 10.1 | Page 20

Observe the following pattern \[1^2 = \frac{1}{6}\left[ 1 \times \left( 1 + 1 \right) \times \left( 2 \times 1 + 1 \right) \right]\]
\[ 1^2 + 2^2 = \frac{1}{6}\left[ 2 \times \left( 2 + 1 \right) \times \left( 2 \times 2 + 1 \right) \right]\]
\[ 1^2 + 2^2 + 3^2 = \frac{1}{6}\left[ 3 \times \left( 3 + 1 \right) \times \left( 2 \times 3 + 1 \right) \right]\]
\[ 1^2 + 2^2 + 3^2 + 4^2 = \frac{1}{6}\left[ 4 \times \left( 4 + 1 \right) \times \left( 2 \times 4 + 1 \right) \right]\] and find the values :  

12 + 22 + 32 + 4+ ... + 102

 

 

Ex. 3.20 | Q 10.2 | Page 20

Observe the following pattern \[1^2 = \frac{1}{6}\left[ 1 \times \left( 1 + 1 \right) \times \left( 2 \times 1 + 1 \right) \right]\]
\[ 1^2 + 2^2 = \frac{1}{6}\left[ 2 \times \left( 2 + 1 \right) \times \left( 2 \times 2 + 1 \right) \right]\]
\[ 1^2 + 2^2 + 3^2 = \frac{1}{6}\left[ 3 \times \left( 3 + 1 \right) \times \left( 2 \times 3 + 1 \right) \right]\]
\[ 1^2 + 2^2 + 3^2 + 4^2 = \frac{1}{6}\left[ 4 \times \left( 4 + 1 \right) \times \left( 2 \times 4 + 1 \right) \right]\] and find the values :  

52 + 62 + 72 + 82 + 92 + 102 + 112 + 122

 

 

Ex. 3.20 | Q 11.1 | Page 20

Which of the following number  square of even number? 

121

 

Ex. 3.20 | Q 11.2 | Page 20

Which of the following number  square of even number? 

 225 

Ex. 3.20 | Q 11.3 | Page 20

Which of the following number is squares of even number ?

256

Ex. 3.20 | Q 11.4 | Page 20

Which of the following number  square of even number?

324 

Ex. 3.20 | Q 11.5 | Page 20

Which of the following number  square of even number? 

1296 

Ex. 3.20 | Q 11.6 | Page 20

Which of the following number are square of even number?

6561

Ex. 3.20 | Q 11.7 | Page 20

Which of the following number  square of even number? 

5476 

Ex. 3.20 | Q 11.8 | Page 20

Which of the following number  square of even number? 

4489

Ex. 3.20 | Q 11.9 | Page 20

Which of the following number  square of even number? 

373758 

Ex. 3.20 | Q 12.1 | Page 20

By just examining the units digit, can you tell which of the following cannot be whole square? 

1026

Ex. 3.20 | Q 12.2 | Page 20

By just examining the unit digis, can you tell which of the following cannot be whole squares? 

 1028

Ex. 3.20 | Q 12.3 | Page 20

By just examining the unit digit, can you tell which of the following cannot be whole square? 

1024 

Ex. 3.20 | Q 12.4 | Page 20

By just examining the unit digit, can you tell which of the following cannot be whole square? 

 1022 

Ex. 3.20 | Q 12.5 | Page 20

By just examining the unit digit, can you tell which of the following cannot be whole square? 

1023

Ex. 3.20 | Q 12.6 | Page 20

By just examining the unit digit, can you tell which of the following cannot be whole square? 

 1027 

Ex. 3.20 | Q 13 | Page 20

Write five numbers for which you cannot decide whether they are squares. 

Ex. 3.20 | Q 14 | Page 20

Write five numbers which you cannot decide whether they are square just by looking at the unit's digit.

Ex. 3.20 | Q 15.1 | Page 20

Write true (T) or false (F) for the following statement. 

The number of digits in a square number is even. 

Ex. 3.20 | Q 15.2 | Page 20

Write true (T) or false (F) for the following statement.

 The square of a prime number is prime. 

Ex. 3.20 | Q 15.3 | Page 20

Write true (T) or false (F) for the following statement. 

 The sum of two square numbers is a square number. 

Ex. 3.20 | Q 15.4 | Page 20

Write true (T) or false (F) for the following statement.  

The difference of two square numbers is a square number 

Ex. 3.20 | Q 15.5 | Page 20

Write true (T) or false (F) for the following statement. 

The product of two square numbers is a square number.

Ex. 3.20 | Q 15.6 | Page 20

Write true (T) or false (F) for the following statement. 

No square number is negative.

Ex. 3.20 | Q 15.7 | Page 20

Write true (T) or false (F) for the following statement .

There is no square number between 50 and 60.

Ex. 3.20 | Q 15.8 | Page 20

Write true (T) or false (F) for the following statement. 

There are fourteen square number upto 200.

Chapter 3: Squares and Square Roots Exercise 3.30 solutions [Page 32]

Ex. 3.30 | Q 1.1 | Page 32

Find the squares of the following numbers using column method. Verify the result by finding the square using the usual multiplication: 

 25

Ex. 3.30 | Q 1.2 | Page 32

Find the squares of the following numbers using column method. Verify the result by finding the square using the usual multiplication: 

37 

Ex. 3.30 | Q 1.3 | Page 32

Find the squares of the following numbers using column method. Verify the result by finding the square using the usual multiplication: 

 54 

Ex. 3.30 | Q 1.4 | Page 32

Find the squares of the following numbers using column method. Verify the result by finding the square using the usual multiplication: 

71 

 

Ex. 3.30 | Q 1.5 | Page 32

Find the squares of the following numbers using column method. Verify the result by finding the square using the usual multiplication: 

96 

Ex. 3.30 | Q 2.1 | Page 32

Find the squares of the following numbers using diagonal method: 

98

Ex. 3.30 | Q 2.2 | Page 32

Find the squares of the following numbers using diagonal method: 

 273

Ex. 3.30 | Q 2.3 | Page 32

Find the squares of the following numbers using diagonal method: 

348 

Ex. 3.30 | Q 2.4 | Page 32

Find the squares of the following numbers using diagonal method: 

295

Ex. 3.30 | Q 2.5 | Page 32

Find the squares of the following numbers using diagonal method:  

 171 

Ex. 3.30 | Q 3.1 | Page 32

Find the square of the following number: 

127 

Ex. 3.30 | Q 3.2 | Page 32

Find the square of the following number: 

503

Ex. 3.30 | Q 3.3 | Page 32

Find the square of the following number: 

451

Ex. 3.30 | Q 3.4 | Page 32

Find the square of the following number: 

862

Ex. 3.30 | Q 3.5 | Page 32

Find the square of the following number: 

265 

Ex. 3.30 | Q 4.1 | Page 32

Find the square of the following number: 

425 

Ex. 3.30 | Q 4.2 | Page 32

Find the square of the following number: 

 575

Ex. 3.30 | Q 4.3 | Page 32

Find the square of the following number: 

 405

Ex. 3.30 | Q 4.4 | Page 32

Find the square of the following number:  

205 

Ex. 3.30 | Q 4.5 | Page 32

Find the square of the following number: 

95 

Ex. 3.30 | Q 4.6 | Page 32

Find the square of the following number: 

745 

Ex. 3.30 | Q 4.7 | Page 32

Find the square of the following number: 

512 

Ex. 3.30 | Q 4.8 | Page 32

Find the square of the following number: 

995 

Ex. 3.30 | Q 5.1 | Page 32

Find the squares of the following numbers using the identity (a + b)2 = a2 + 2ab + b2:  

 405

Ex. 3.30 | Q 5.2 | Page 32

Find the squares of the following number using the identity (a + b)2 = a2 + 2ab + b2:  

 510 

Ex. 3.30 | Q 5.3 | Page 32

Find the squares of the following number using the identity (a + b)2 = a2 + 2ab + b

1001 

Ex. 3.30 | Q 5.4 | Page 32

Find the square of the following numbers using the identity (a + b)2 = a2 + 2ab + b2

 209 

Ex. 3.30 | Q 5.5 | Page 32

Find the squares of the following numbers using the identity (a + b)2 = a2 + 2ab + b2

605

Ex. 3.30 | Q 6.1 | Page 32

Find the square of the following number using the identity (a − b)2 = a2 − 2ab + b2

395 

Ex. 3.30 | Q 6.2 | Page 32

Find the square of the following number using the identity (a − b)2 = a2 − 2ab + b2:  

 995 

Ex. 3.30 | Q 6.3 | Page 32

Find the square of the following number using the identity (a − b)2 = a2 − 2ab + b2

495 

Ex. 3.30 | Q 6.4 | Page 32

Find the squares of the following numbers using the identity (a − b)2 = a2 − 2ab + b2

 498 

Ex. 3.30 | Q 6.5 | Page 32

Find the square of the following number using the identity (a − b)2 = a2 − 2ab + b2:  

99 

Ex. 3.30 | Q 6.6 | Page 32

Find the square of the following number using the identity (a − b)2 = a2 − 2ab + b2:  

999

Ex. 3.30 | Q 6.7 | Page 32

Find the square of the following number using the identity (a − b)2 = a2 − 2ab + b2:  

599

Ex. 3.30 | Q 7.1 | Page 32

Find the squares of the following numbers by visual method: 

52

Ex. 3.30 | Q 7.2 | Page 32

Find the square of the following number by visual method:  

95 

Ex. 3.30 | Q 7.3 | Page 32

Find the square of the following number by visual method:

 505 

Ex. 3.30 | Q 7.4 | Page 32

Find the square of the following number by visual method:

 702

Ex. 3.30 | Q 7.5 | Page 32

Find the square of the following number by visual method: 

99 

Chapter 3: Squares and Square Roots Exercise 3.40 solutions [Page 38]

Ex. 3.40 | Q 1.1 | Page 38

Write the possible unit's digits of the square root of the following numbers\. Which of these number is odd square root? 

 9801 

Ex. 3.40 | Q 1.2 | Page 38

Write the possible unit's digits of the square root of the following number. Which of these number is odd square root?

 99856 

Ex. 3.40 | Q 1.3 | Page 38

Write the possible unit's digit of the square root of the following number. Which of these number  odd square root?  

998001 

Ex. 3.40 | Q 1.4 | Page 38

Write the possible unit's digit of the square root of the following number. Which of these number is odd square root? 

657666025 

Ex. 3.40 | Q 2.01 | Page 38

Find the square root of each of the following by prime factorization. 

441 

Ex. 3.40 | Q 2.02 | Page 38

Find the square root the following by prime factorization. 

 196 

Ex. 3.40 | Q 2.03 | Page 38

Find the square root  the following by prime factorization. 

529 

Ex. 3.40 | Q 2.04 | Page 38

Find the square root  the following by prime factorization. 

 1764 

Ex. 3.40 | Q 2.05 | Page 38

Find the square root the following by prime factorization. 

1156

Ex. 3.40 | Q 2.06 | Page 38

Find the square root  the following by prime factorization. 

 4096 

Ex. 3.40 | Q 2.07 | Page 38

Find the square root the following by prime factorization.  

 7056

Ex. 3.40 | Q 2.08 | Page 38

Find the square root  the following by prime factorization.

 8281

Ex. 3.40 | Q 2.09 | Page 38

Find the square rootthe following by prime factorization.  

11664 

Ex. 3.40 | Q 2.1 | Page 38

Find the square root  the following by prime factorization.  

 47089

Ex. 3.40 | Q 2.11 | Page 38

Find the square root the following by prime factorization. 

24336 

Ex. 3.40 | Q 2.12 | Page 38

Find the square root  the following by prime factorization. 

 190969

Ex. 3.40 | Q 2.13 | Page 38

Find the square root the following by prime factorization. 

586756 

Ex. 3.40 | Q 2.14 | Page 38

Find the square root  the following by prime factorization. 

27225

Ex. 3.40 | Q 2.15 | Page 38

Find the square root the following by prime factorization. 

3013696

Ex. 3.40 | Q 3 | Page 38

Find the smallest number by which 180 must be multiplied so that it becomes a perfect square. Also, find the square root of the perfect square so obtained.

Ex. 3.40 | Q 4 | Page 38

Find the smallest number by which 147 must be multiplied so that it becomes a perfect square. Also, find the square root of the number so obtained.

Ex. 3.40 | Q 5 | Page 38

Find the smallest number by which 3645 must be divided so that it becomes a perfect square. Also, find the square root of the resulting number. 

 

Ex. 3.40 | Q 6 | Page 38

Find the smallest number by which 1152 must be divided so that it becomes a perfect square. Also, find the square root of the number so obtained.

Ex. 3.40 | Q 7 | Page 38

The product of two numbers is 1296. If one number is 16 times the other, find the numbers.

Ex. 3.40 | Q 8 | Page 38

A welfare association collected Rs 202500 as donation from the residents. If each paid as many rupees as there were residents, find the number of residents.

Ex. 3.40 | Q 9 | Page 38

A society collected Rs 92.16. Each member collected as many paise as there were members. How many members were there and how much did each contribute? 

Ex. 3.40 | Q 10 | Page 38

A school collected Rs 2304 as fees from its students. If each student paid as many paise as there were students in the school, how many students were there in the school? 

Ex. 3.40 | Q 11 | Page 38

The area of a square field is 5184 cm2. A rectangular field, whose length is twice its breadth has its perimeter equal to the perimeter of the square field. Find the area of the rectangular field.

Ex. 3.40 | Q 12.1 | Page 38

Find the least square number, exactly divisible by each one of the numbers:
(i) 6, 9, 15 and 20

Ex. 3.40 | Q 12.2 | Page 38

Find the least square number, exactly divisible by each one of the number: 

8, 12, 15 and 20

Ex. 3.40 | Q 13 | Page 38

Find the square roots of 121 and 169 by the method of repeated subtraction. 

 

Ex. 3.40 | Q 14.1 | Page 38

Write the prime factorization of the following number and hence find their square root. 

 7744

Ex. 3.40 | Q 14.2 | Page 38

Write the prime factorization of the following number and hence find their square root. 

9604 

Ex. 3.40 | Q 14.3 | Page 38

Write the prime factorization of the following number and hence find their square root. 

5929 

Ex. 3.40 | Q 14.4 | Page 38

Write the prime factorization of the following number and hence find their square root. 

7056

Ex. 3.40 | Q 15 | Page 38

The students of class VIII of a school donated Rs 2401 for PM's National Relief Fund. Each student donated as many rupees as the number of students in the class. Find the number of students in the class. 

Ex. 3.40 | Q 16 | Page 38

A PT teacher wants to arrange maximum possible number of 6000 students in a field such that the number of rows is equal to the number of columns. Find the number of rows if 71 were left out after arrangement.

Chapter 3: Squares and Square Roots Exercise 3.50 solutions [Pages 43 - 44]

Ex. 3.50 | Q 1.01 | Page 43

Find the square  of the following by long division method: 

12544 

 

 

Ex. 3.50 | Q 1.02 | Page 43

Find the square root  the following by long division method: 

97344

Ex. 3.50 | Q 1.03 | Page 43

Find the square root  the following by long division method: 

 286225 

Ex. 3.50 | Q 1.04 | Page 43

Find the square root the following by long division method: 

390625

Ex. 3.50 | Q 1.05 | Page 43

Find the square root  the following by long division method: 

363609

Ex. 3.50 | Q 1.06 | Page 43

Find the square root the following by long division method:

974169

Ex. 3.50 | Q 1.07 | Page 43

Find the square root the following by long division method: 

120409

Ex. 3.50 | Q 1.08 | Page 43

Find the square root  the following by long division method: 

 1471369

Ex. 3.50 | Q 1.09 | Page 43

Find the square root  the following by long division method: 

291600

Ex. 3.50 | Q 1.1 | Page 43

Find the square root the following by long division method: 

9653449

Ex. 3.50 | Q 1.11 | Page 43

Find the square root the following by long division method:  

1745041

 

Ex. 3.50 | Q 1.12 | Page 43

Find the square root of each of the following by long division method: 

 4008004

Ex. 3.50 | Q 1.13 | Page 43

Find the square root  the following by long division method: 

20657025

Ex. 3.50 | Q 1.14 | Page 43

Find the square root  the following by long division method:

152547201

Ex. 3.50 | Q 1.15 | Page 43

Find the square root the following by long division method: 

20421361

 

Ex. 3.50 | Q 1.16 | Page 43

Find the square root the following by long division method: 

 62504836

Ex. 3.50 | Q 1.17 | Page 43

Find the square root the following by long division method: 

 82264900

Ex. 3.50 | Q 1.18 | Page 43

Find the square root  the following by long division method: 

3226694416 

Ex. 3.50 | Q 1.19 | Page 43

Find the square root the following by long division method:

6407522209

Ex. 3.50 | Q 1.2 | Page 43

Find the square root  the following by long division method: 

3915380329

Ex. 3.50 | Q 2.1 | Page 43

Find the least number which must be subtracted from the following numbers to make them a perfect square: 

 2361

Ex. 3.50 | Q 2.2 | Page 43

Find the least number which must be subtracted from the following numbers to make them a perfect square:

 194491

 

Ex. 3.50 | Q 2.3 | Page 43

Find the least number which must be subtracted from the following numbers to make them a perfect square: 

26535

Ex. 3.50 | Q 2.4 | Page 43

Find the least number which must be subtracted from the following numbers to make them a perfect square:

16160

 

Ex. 3.50 | Q 2.5 | Page 43

Find the least number which must be subtracted from the following numbers to make them a perfect square: 

4401624

Ex. 3.50 | Q 3.1 | Page 43

Find the least number which must be added to the following numbers to make them a perfect square:

 5607

Ex. 3.50 | Q 3.2 | Page 43

Find the least number which must be added to the following numbers to make them a perfect square:

4931 

 

Ex. 3.50 | Q 3.3 | Page 43

Find the least number which must be added to the following numbers to make them a perfect square:

4515600

Ex. 3.50 | Q 3.4 | Page 43

Find the least number which must be added to the following numbers to make them a perfect square:

37460

Ex. 3.50 | Q 3.5 | Page 43

Find the least number which must be added to the following numbers to make them a perfect square:

506900

Ex. 3.50 | Q 4 | Page 43

Find the greatest number of 5 digits which is a perfect square.

 

Ex. 3.50 | Q 5 | Page 43

Find the least number of 4 digits which is a perfect square.

Ex. 3.50 | Q 6 | Page 43

Find the least number of six digits which is a perfect square.

 

Ex. 3.50 | Q 7 | Page 44

Find the greatest number of 4 digits which is a perfect square.

Ex. 3.50 | Q 8 | Page 44

A General arranges his soldiers in rows to form a perfect square. He finds that in doing so, 60 soldiers are left out. If the total number of soldiers be 8160, find the number of soldiers in each row.

Ex. 3.50 | Q 9 | Page 44

The area of a square field is 60025 m2. A man cycles along its boundary at 18 km/hr. In how much time will he return at the starting point?

Ex. 3.50 | Q 10 | Page 44

The cost of levelling and turfing a square lawn at Rs 2.50 per m2 is Rs 13322.50. Find the cost of fencing it at Rs 5 per metre. 

Ex. 3.50 | Q 11 | Page 44

Find the greatest number of three digits which is a perfect square.

 

Ex. 3.50 | Q 12 | Page 44

Find the smallest number which must be added to 2300 so that it becomes a perfect square.

Chapter 3: Squares and Square Roots Exercise 3.60 solutions [Pages 48 - 49]

Ex. 3.60 | Q 1.01 | Page 48

Find the square root of:

\[\frac{441}{961}\] 

Ex. 3.60 | Q 1.02 | Page 48

Find the square root of:

\[\frac{324}{841}\]

Ex. 3.60 | Q 1.03 | Page 48

Find the square root of:

\[4\frac{29}{29}\]

Ex. 3.60 | Q 1.04 | Page 48

Find the square root of:

\[2\frac{14}{25}\]

Ex. 3.60 | Q 1.05 | Page 48

Find the square root of:

\[23\frac{26}{121}\]

Ex. 3.60 | Q 1.06 | Page 48

Find the square root of:

\[23\frac{26}{121}\]

Ex. 3.60 | Q 1.07 | Page 48

Find the square root of:

\[25\frac{544}{729}\]

Ex. 3.60 | Q 1.08 | Page 48

Find the square root of:

\[75\frac{46}{49}\]

Ex. 3.60 | Q 1.09 | Page 48

Find the square root of:

\[3\frac{942}{2209}\]

Ex. 3.60 | Q 1.1 | Page 48

Find the square root of:

\[3\frac{334}{3025}\]

Ex. 3.60 | Q 1.11 | Page 48

Find the square root of:

\[21\frac{2797}{3364}\]

Ex. 3.60 | Q 1.12 | Page 48

Find the square root of:

\[38\frac{11}{25}\]

Ex. 3.60 | Q 1.13 | Page 48

Find the square root of:

\[23\frac{394}{729}\]

Ex. 3.60 | Q 1.14 | Page 48

Find the square root of:

\[21\frac{51}{169}\]

Ex. 3.60 | Q 1.15 | Page 48

Find the square root of:

\[10\frac{151}{225}\]

 

Ex. 3.60 | Q 2.1 | Page 48

Find the value of:

\[\frac{\sqrt{80}}{\sqrt{405}}\]

Ex. 3.60 | Q 2.2 | Page 48

Find the value of:

\[\frac{\sqrt{441}}{\sqrt{625}}\]

 

Ex. 3.60 | Q 2.3 | Page 48

Find the value of:

\[\frac{\sqrt{1587}}{\sqrt{1728}}\]

Ex. 3.60 | Q 2.4 | Page 48

Find the value of:

\[\sqrt{72} \times \sqrt{338}\]

 

Ex. 3.60 | Q 2.5 | Page 48

Find the value of:

\[\sqrt{45} \times \sqrt{20}\]

Ex. 3.60 | Q 3 | Page 48

The area of a square field is \[80\frac{244}{729}\] square metres. Find the length of each side of the field.

Ex. 3.60 | Q 4 | Page 49

The area of a square field is \[30\frac{1}{4} m^2 .\] Calculate the length of the side of the square.

Ex. 3.60 | Q 5 | Page 49

Find the length of a side of a square playground whose area is equal to the area of a rectangular field of diamensions 72 m and 338 m. 

Chapter 3: Squares and Square Roots Exercise 3.70 solutions [Page 52]

Ex. 3.70 | Q 1 | Page 52

Find the square root in decimal form:
84.8241

Ex. 3.70 | Q 2 | Page 52

Find the square root in decimal form:
0.7225

Ex. 3.70 | Q 3 | Page 52

Find the square root in decimal form:
0.813604

Ex. 3.70 | Q 4 | Page 52

Find the square root in decimal form:
0.00002025

Ex. 3.70 | Q 5 | Page 52

Find the square root in decimal form:
150.0625 

Ex. 3.70 | Q 6 | Page 52

Find the square root in decimal form:
225.6004

Ex. 3.70 | Q 7 | Page 52

Find the square root in decimal form:
3600.720036 

Ex. 3.70 | Q 8 | Page 52

Find the square root in decimal form:
236.144689

Ex. 3.70 | Q 9 | Page 52

Find the square root in decimal form:
0.00059049 

Ex. 3.70 | Q 10 | Page 52

Find the square root in decimal form:
176.252176

Ex. 3.70 | Q 11 | Page 52

Find the square root in decimal form:
9998.0001

Ex. 3.70 | Q 12 | Page 52

Find the square root in decimal form:
0.00038809

Ex. 3.70 | Q 13 | Page 52

What is that fraction which when multiplied by itself gives 227.798649?

 

Ex. 3.70 | Q 14 | Page 52

The area of a square playground is 256.6404 square metres. Find the length of one side of the playground.

Ex. 3.70 | Q 15 | Page 52

What is the fraction which when multiplied by itself gives 0.00053361?

Ex. 3.70 | Q 16.1 | Page 52

Simplify: 

`(sqrt59.29-sqrt5.29)/(sqrt59.29+sqrt5.29)`

 

Ex. 3.70 | Q 16.2 | Page 52

Simplify:

`(sqrt0.2304+sqrt0.1764)/(sqrt0.2304-sqrt0.1764)`

Ex. 3.70 | Q 17 | Page 52

Evaluate   `sqrt(50625)`and hence find the value of `sqrt506.25+sqrt5.0625`

Ex. 3.70 | Q 18 | Page 52

Find the value of `sqrt (103.0225)`nd hence find the value of

`sqrt(10.302.25)` 

`sqrt(1.030225)`

Chapter 3: Squares and Square Roots Exercise 3.80 solutions [Pages 56 - 57]

Ex. 3.80 | Q 1.01 | Page 56

Find the square root the following correct to three places of decimal.

Ex. 3.80 | Q 1.02 | Page 56

Find the square root the following correct to three places of decimal. 

7

Ex. 3.80 | Q 1.03 | Page 56

Find the square root  the following correct to three places of decimal. 

17

Ex. 3.80 | Q 1.04 | Page 56

Find the square root  the following correct to three places of decimal. 

20

Ex. 3.80 | Q 1.05 | Page 56

Find the square root  the following correct to three places of decimal.

 66

Ex. 3.80 | Q 1.06 | Page 56

Find the square root  the following correct to three places of decimal.

 427

Ex. 3.80 | Q 1.07 | Page 56

Find the square root  the following correct to three places of decimal. 

1.7

Ex. 3.80 | Q 1.08 | Page 56

Find the square root the following correct to three places of decimal. 

23.1

Ex. 3.80 | Q 1.09 | Page 56

Find the square root the following correct to three places of decimal. 

 2.5

Ex. 3.80 | Q 1.1 | Page 56

Find the square root  the following correct to three places of decimal.

 237.615

Ex. 3.80 | Q 1.11 | Page 56

Find the square root  the following correct to three places of decimal. 

15.3215

Ex. 3.80 | Q 1.12 | Page 56

Find the square root the following correct to three places of decimal. 

 0.9

 

Ex. 3.80 | Q 1.13 | Page 56

Find the square root  the following correct to three places of decimal.

 0.1

Ex. 3.80 | Q 1.14 | Page 56

Find the square root the following correct to three places of decimal. 

0.016

Ex. 3.80 | Q 1.15 | Page 56

Find the square root the following correct to three places of decimal. 

 0.00064

 

Ex. 3.80 | Q 1.16 | Page 56

Find the square root  the following correct to three places of decimal. 

0.019

Ex. 3.80 | Q 1.17 | Page 56

Find the square root the following correct to three places of decimal. 

`7/8`

Ex. 3.80 | Q 1.18 | Page 56

Find the square root  the following correct to three places of decimal. 

`5/12` 

Ex. 3.80 | Q 1.19 | Page 56

Find the square rootthe following correct to three places of decimal. 

`2 1/2`

Ex. 3.80 | Q 1.2 | Page 56

Find the square root  the following correct to three places of decimal. 

`287 5/8` 

 

Ex. 3.80 | Q 2 | Page 57

Find the square root of 12.0068 correct to four decimal places.

 

Ex. 3.80 | Q 3 | Page 57

Find the square root of 11 correct to five decimal places.

 

Ex. 3.80 | Q 4.1 | Page 57

Given that: \[\sqrt{2} = 1 . 414, \sqrt{3} = 1 . 732, \sqrt{5} = 2 . 236 \text { and }\sqrt{7} = 2 . 646,\] evaluate  the following: 

\[\sqrt{\frac{144}{7}}\] 

Ex. 3.80 | Q 4.2 | Page 57

Given that: \[\sqrt{2} = 1 . 414, \sqrt{3} = 1 . 732, \sqrt{5} = 2 . 236 \text{ and } \sqrt{7} = 2 . 646,\]evaluate the following: 

\[\sqrt{\frac{2500}{3}}\]

Ex. 3.80 | Q 5.1 | Page 57

Given that: 

\[\sqrt{2} = 1 . 414, \sqrt{3} = 1 . 732, \sqrt{5} = 2 . 236 \text{ and } \sqrt{7} = 2 . 646,\]ind the square roots of the following: 

\[\frac{196}{75}\]

Ex. 3.80 | Q 5.2 | Page 57

Given that: 

\[\sqrt{2} = 1 . 414, \sqrt{3} = 1 . 732, \sqrt{5} = 2 . 236 \text{ and } \sqrt{7} = 2 . 646,\]  find the square roots of the following: 

\[\frac{400}{63}\]

Ex. 3.80 | Q 5.3 | Page 57

Given that: \[\sqrt{2} = 1 . 414, \sqrt{3} = 1 . 732, \sqrt{5} = 2 . 236 \text{ and } \sqrt{7} = 2 . 646,\] find the square roots of the following:

\[\frac{150}{7}\]

Ex. 3.80 | Q 5.4 | Page 57

Given that: 

\[\sqrt{2} = 1 . 414, \sqrt{3} = 1 . 732, \sqrt{5} = 2 . 236 \text{ and } \sqrt{7} = 2 . 646,\] 

\[\frac{256}{5}\]

Ex. 3.80 | Q 5.5 | Page 57

Given that: \[\sqrt{2} = 1 . 414, \sqrt{3} = 1 . 732, \sqrt{5} = 2 . 236 \text{ and } \sqrt{7} = 2 . 646,\]  find the square root of the following:

\[\frac{25}{50}\] 

Chapter 3: Squares and Square Roots Exercise 3.90 solutions [Page 61]

Ex. 3.90 | Q 1 | Page 61

Using square root table, find the square root

Ex. 3.90 | Q 2 | Page 61

Using square root table, find the square root
15 

Ex. 3.90 | Q 3 | Page 61

Using square root table, find the square root
74 

Ex. 3.90 | Q 4 | Page 61

Using square root table, find the square root
82 

Ex. 3.90 | Q 5 | Page 61

Using square root table, find the square root
198 

Ex. 3.90 | Q 6 | Page 61

Using square root table, find the square root
540 

Ex. 3.90 | Q 7 | Page 61

Using square root table, find the square root
8700

 

Ex. 3.90 | Q 8 | Page 61

Using square root table, find the square root
3509 

Ex. 3.90 | Q 9 | Page 61

Using square root table, find the square root
6929 

Ex. 3.90 | Q 10 | Page 61

Using square root table, find the square root
25725 

Ex. 3.90 | Q 11 | Page 61

Using square root table, find the square root
1312 

 

Ex. 3.90 | Q 12 | Page 61

Using square root table, find the square root
4192 

Ex. 3.90 | Q 13 | Page 61

Using square root table, find the square root
4955 

Ex. 3.90 | Q 14 | Page 61

Using square root table, find the square root \[\frac{99}{144}\] 

Ex. 3.90 | Q 15 | Page 61

Using square root table, find the square root \[\frac{57}{169}\] 

Ex. 3.90 | Q 16 | Page 61

Using square root table, find the square root \[\frac{101}{169}\] 

Ex. 3.90 | Q 17 | Page 61

Using square root table, find the square root
13.21 

Ex. 3.90 | Q 18 | Page 61

Using square root table, find the square root 

Ex. 3.90 | Q 19 | Page 61

Using square root table, find the square root
110 

Ex. 3.90 | Q 20 | Page 61

Using square root table, find the square root
1110 

Ex. 3.90 | Q 21 | Page 61

Using square root table, find the square root
11.11

Ex. 3.90 | Q 22 | Page 61

The area of a square field is 325 m2. Find the approximate length of one side of the field. 

Ex. 3.90 | Q 23 | Page 61

Find the length of a side of a sqiare, whose area is equal to the area of a rectangle with sides 240 m and 70 m. 

Chapter 3: Squares and Square Roots

Ex. 3.10Ex. 3.20Ex. 3.30Ex. 3.40Ex. 3.50Ex. 3.60Ex. 3.70Ex. 3.80Ex. 3.90

RD Sharma Mathematics Class 8 by R D Sharma (2019-2020 Session)

Mathematics for Class 8 by R D Sharma (2019-2020 Session) - Shaalaa.com

RD Sharma solutions for Class 8 Mathematics chapter 3 - Squares and Square Roots

RD Sharma solutions for Class 8 Maths chapter 3 (Squares and Square Roots) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics for Class 8 by R D Sharma (2019-2020 Session) solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. RD Sharma textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 8 Mathematics chapter 3 Squares and Square Roots are Introduction of Square Numbers, Properties of Square Numbers, Some More Interesting Patterns, Finding the Square of a Number - Other Patterns in Squares, Finding the Square of a Number - Pythagorean Triplets, Square Roots - Finding Square Roots, Square Roots - Finding Square Root Through Repeated Subtraction, Square Roots - Finding Square Root Through Prime Factorisation, Square Roots - Finding Square Root by Division Method, Square Roots of Decimals, Estimating Square Root.

Using RD Sharma Class 8 solutions Squares and Square Roots exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in RD Sharma Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 8 prefer RD Sharma Textbook Solutions to score more in exam.

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