#### Chapters

Chapter 2: Powers

Chapter 3: Squares and Square Roots

Chapter 4: Cubes and Cube Roots

Chapter 5: Playing with Numbers

Chapter 6: Algebraic Expressions and Identities

Chapter 7: Factorization

Chapter 8: Division of Algebraic Expressions

Chapter 9: Linear Equation in One Variable

Chapter 10: Direct and Inverse Variations

Chapter 11: Time and Work

Chapter 12: Percentage

Chapter 13: Proft, Loss, Discount and Value Added Tax (VAT)

Chapter 14: Compound Interest

Chapter 15: Understanding Shapes-I (Polygons)

Chapter 16: Understanding Shapes-II (Quadrilaterals)

Chapter 17: Understanding Shapes-III (Special Types of Quadrilaterals)

Chapter 18: Practical Geometry (Constructions)

Chapter 19: Visualising Shapes

Chapter 20: Mensuration - I (Area of a Trapezium and a Polygon)

Chapter 21: Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube)

Chapter 22: Mensuration - III (Surface Area and Volume of a Right Circular Cylinder)

Chapter 23: Data Handling-I (Classification and Tabulation of Data)

Chapter 24: Data Handling-II (Graphical Representation of Data as Histograms)

Chapter 25: Data Handling-III (Pictorial Representation of Data as Pie Charts or Circle Graphs)

Chapter 26: Data Handling-IV (Probability)

Chapter 27: Introduction to Graphs

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

## Chapter 3: Squares and Square Roots

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

Which of the following numbers are perfect squares?

484

Which of the following numbers are perfect squares?

625

Which of the following numbers are perfect squares?

576

Which of the following numbers are perfect squares?

941

Which of the following numbers are perfect squares?

961

Which of the following numbers are perfect squares?

2500

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

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

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

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

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

23805

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

12150

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

7688

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

14283

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

1800

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

2904

Which of the following numbers are perfect square?

11

Which of the following numbers are perfect square?

12

Which of the following numbers are perfect square?

16

Which of the following numbers are perfect square?

32

Which of the following numbers are perfect squares?

36

Which of the following numbers are perfect square?

50

Which of the following numbers are perfect square?

64

Which of the following numbers are perfect square?

79

Which of the following numbers are perfect square?

81

Which of the following numbers are perfect square?

111

Which of the following numbers are perfect square?

121

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

189,

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

225

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

2048

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

343

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

441

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

2916

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

11025

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

3549

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

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

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

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

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

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

7776

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

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

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

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

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

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

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

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

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

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]

The following number are not perfect squares. Give reason.

1547

The following number is not perfect square. Give reason.

45743

The following number is not perfect square. Give reason.

8948

The following number is not perfect square. Give reason.

333333

Show that the following number is not perfect square:

9327

Show that the following number is not perfect square:

4058

Show that the following number is not perfect square:

22453

Show that the following number is not perfect square:

743522

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

731

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

3456

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

5559

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

42008

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

52

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

977

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

4583

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

78367

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

52698

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

99880

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

12796

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

55555

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

53924

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 =* *n*^{2}, where the left hand side consists of *n* terms.

Observe the following pattern

2^{2} − 1^{2} = 2 + 1

3^{2} − 2^{2} = 3 + 2

4^{2} − 3^{2} = 4 + 3

5^{2} − 4^{2} = 5 + 4

and find the value of

100^{2} − 99^{2}

Observe the following pattern

2^{2} − 1^{2} = 2 + 1

3^{2} − 2^{2} = 3 + 2

4^{2} − 3^{2} = 4 + 3

5^{2} − 4^{2} = 5 + 4

and find the value of

111^{2} − 109^{2}

Observe the following pattern

2^{2} − 1^{2} = 2 + 1

3^{2} − 2^{2} = 3 + 2

4^{2} − 3^{2} = 4 + 3

5^{2} − 4^{2} = 5 + 4

and find the value of

99^{2} − 96^{2}

Which of the following triplets are pythagorean?

(8, 15, 17)

Which of the following triplet is pythagorean?

(18, 80, 82)

Which of the following triplet pythagorean?

(14, 48, 51)

Which of the following triplet pythagorean?

(10, 24, 26)

Which of the following triplet pythagorean?

(16, 63, 65)

Which of the following triplet pythagorean?

(12, 35, 38)

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)

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

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

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 :

1^{2} + 2^{2} + 3^{2} + 4^{2 }+ ... + 10^{2}

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 :

5^{2} + 6^{2} + 7^{2} + 8^{2} + 9^{2} + 10^{2} + 11^{2} + 12^{2}

Which of the following number square of even number?

121

Which of the following number square of even number?

225

Which of the following number is squares of even number ?

256

Which of the following number square of even number?

324

Which of the following number square of even number?

1296

Which of the following number are square of even number?

6561

Which of the following number square of even number?

5476

Which of the following number square of even number?

4489

Which of the following number square of even number?

373758

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

1026

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

1028

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

1024

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

1022

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

1023

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

1027

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

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

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

The number of digits in a square number is even.

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

The square of a prime number is prime.

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

The sum of two square numbers is a square number.

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

The difference of two square numbers is a square number

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

The product of two square numbers is a square number.

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

No square number is negative.

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

There is no square number between 50 and 60.

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]

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

25

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

37

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

54

71

96

Find the squares of the following numbers using diagonal method:

98

Find the squares of the following numbers using diagonal method:

273

Find the squares of the following numbers using diagonal method:

348

Find the squares of the following numbers using diagonal method:

295

Find the squares of the following numbers using diagonal method:

171

Find the square of the following number:

127

Find the square of the following number:

503

Find the square of the following number:

451

Find the square of the following number:

862

Find the square of the following number:

265

Find the square of the following number:

425

Find the square of the following number:

575

Find the square of the following number:

405

Find the square of the following number:

205

Find the square of the following number:

95

Find the square of the following number:

745

Find the square of the following number:

512

Find the square of the following number:

995

Find the squares of the following numbers using the identity (*a* + *b*)^{2} = *a*^{2} + 2*ab* + *b*^{2}:

405

Find the squares of the following number using the identity (*a* + *b*)^{2} = *a*^{2} + 2*ab* + *b*^{2}:

510

Find the squares of the following number using the identity (*a* + *b*)^{2} = *a*^{2} + 2*ab* + *b*^{2 }

^{1001 }

Find the square of the following numbers using the identity (*a* + *b*)^{2} = *a*^{2} + 2*ab* + *b*^{2}:

209

Find the squares of the following numbers using the identity (*a* + *b*)^{2} = *a*^{2} + 2*ab* + *b*^{2}:

605

Find the square of the following number using the identity (*a* − *b*)^{2} = *a*^{2} − 2*ab* + *b*^{2}:

395

Find the square of the following number using the identity (*a* − *b*)^{2} = *a*^{2} − 2*ab* + *b*^{2}:

995

Find the square of the following number using the identity (*a* − *b*)^{2} = *a*^{2} − 2*ab* + *b*^{2}:

495

Find the squares of the following numbers using the identity (*a* − *b*)^{2} = *a*^{2} − 2*ab* + *b*^{2}:

498

Find the square of the following number using the identity (*a* − *b*)^{2} = *a*^{2} − 2*ab* + *b*^{2}:

99

Find the square of the following number using the identity (*a* − *b*)^{2} = *a*^{2} − 2*ab* + *b*^{2}:

999

Find the square of the following number using the identity (*a* − *b*)^{2} = *a*^{2} − 2*ab* + *b*^{2}:

599

Find the squares of the following numbers by visual method:

52

Find the square of the following number by visual method:

95

Find the square of the following number by visual method:

505

Find the square of the following number by visual method:

702

Find the square of the following number by visual method:

99

#### Chapter 3: Squares and Square Roots Exercise 3.40 solutions [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

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

99856

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

998001

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

657666025

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

441

Find the square root the following by prime factorization.

196

Find the square root the following by prime factorization.

529

Find the square root the following by prime factorization.

1764

Find the square root the following by prime factorization.

1156

Find the square root the following by prime factorization.

4096

Find the square root the following by prime factorization.

7056

Find the square root the following by prime factorization.

8281

Find the square rootthe following by prime factorization.

11664

Find the square root the following by prime factorization.

47089

Find the square root the following by prime factorization.

24336

Find the square root the following by prime factorization.

190969

Find the square root the following by prime factorization.

586756

Find the square root the following by prime factorization.

27225

Find the square root the following by prime factorization.

3013696

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.

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.

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.

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.

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

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.

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?

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?

The area of a square field is 5184 cm^{2}. 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.

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

(i) 6, 9, 15 and 20

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

8, 12, 15 and 20

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

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

7744

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

9604

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

5929

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

7056

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.

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]

Find the square of the following by long division method:

12544

Find the square root the following by long division method:

97344

Find the square root the following by long division method:

286225

Find the square root the following by long division method:

390625

Find the square root the following by long division method:

363609

Find the square root the following by long division method:

974169

Find the square root the following by long division method:

120409

Find the square root the following by long division method:

1471369

Find the square root the following by long division method:

291600

Find the square root the following by long division method:

9653449

Find the square root the following by long division method:

1745041

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

4008004

Find the square root the following by long division method:

20657025

Find the square root the following by long division method:

152547201

Find the square root the following by long division method:

20421361

Find the square root the following by long division method:

62504836

Find the square root the following by long division method:

82264900

Find the square root the following by long division method:

3226694416

Find the square root the following by long division method:

6407522209

Find the square root the following by long division method:

3915380329

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

2361

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

194491

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

26535

16160

4401624

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

5607

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

4931

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

4515600

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

37460

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

506900

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

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

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

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

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.

The area of a square field is 60025 m^{2}. A man cycles along its boundary at 18 km/hr. In how much time will he return at the starting point?

The cost of levelling and turfing a square lawn at Rs 2.50 per m^{2} is Rs 13322.50. Find the cost of fencing it at Rs 5 per metre.

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

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]

Find the square root of:

\[\frac{441}{961}\]

Find the square root of:

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

Find the square root of:

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

Find the square root of:

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

Find the square root of:

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

Find the square root of:

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

Find the square root of:

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

Find the square root of:

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

Find the square root of:

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

Find the square root of:

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

Find the square root of:

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

Find the square root of:

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

Find the square root of:

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

Find the square root of:

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

Find the square root of:

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

Find the value of:

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

Find the value of:

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

Find the value of:

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

Find the value of:

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

Find the value of:

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

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

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

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]

Find the square root in decimal form:

84.8241

Find the square root in decimal form:

0.7225

Find the square root in decimal form:

0.813604

Find the square root in decimal form:

0.00002025

Find the square root in decimal form:

150.0625

Find the square root in decimal form:

225.6004

Find the square root in decimal form:

3600.720036

Find the square root in decimal form:

236.144689

Find the square root in decimal form:

0.00059049

Find the square root in decimal form:

176.252176

Find the square root in decimal form:

9998.0001

Find the square root in decimal form:

0.00038809

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

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

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

Simplify:

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

Simplify:

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

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

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]

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

5

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

7

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

17

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

20

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

66

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

427

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

1.7

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

23.1

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

2.5

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

237.615

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

15.3215

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

0.9

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

0.1

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

0.016

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

0.00064

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

0.019

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

`7/8`

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

`5/12`

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

`2 1/2`

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

`287 5/8`

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

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

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

\[\sqrt{\frac{144}{7}}\]

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

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

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:

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

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:

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

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:

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

Given that:

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

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

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]

Using square root table, find the square root

7

Using square root table, find the square root

15

Using square root table, find the square root

74

Using square root table, find the square root

82

Using square root table, find the square root

198

Using square root table, find the square root

540

Using square root table, find the square root

8700

Using square root table, find the square root

3509

Using square root table, find the square root

6929

Using square root table, find the square root

25725

Using square root table, find the square root

1312

Using square root table, find the square root

4192

Using square root table, find the square root

4955

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

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

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

Using square root table, find the square root

13.21

Using square root table, find the square root

Using square root table, find the square root

110

Using square root table, find the square root

1110

Using square root table, find the square root

11.11

The area of a square field is 325 m^{2}. Find the approximate length of one side of the field.

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

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

#### Textbook solutions for Class 8

## 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.

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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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