# NCERT solutions for Mathematics Exemplar Class 8 chapter 3 - Square-Square Root and Cube-Cube Root [Latest edition]

#### Chapters ## Chapter 3: Square-Square Root and Cube-Cube Root

Exercise
Exercise [Pages 88 - 97]

### NCERT solutions for Mathematics Exemplar Class 8 Chapter 3 Square-Square Root and Cube-Cube Root Exercise [Pages 88 - 97]

#### Choose the correct alternative:

Exercise | Q 1 | Page 88

196 is the square of ______.

• 11

• 12

• 14

• 16

Exercise | Q 2 | Page 88

Which of the following is a square of an even number?

• 144

• 169

• 441

• 625

Exercise | Q 3 | Page 88

A number ending in 9 will have the units place of its square as ______.

• 3

• 9

• 1

• 6

Exercise | Q 4 | Page 89

Which of the following will have 4 at the units place?

• 142

• 62

• 27

• 35

Exercise | Q 5 | Page 89

How many natural numbers lie between 52 and 62?

• 9

• 10

• 11

• 12

Exercise | Q 6 | Page 89

Which of the following cannot be a perfect square?

• 841

• 529

• 198

• All of these

Exercise | Q 7 | Page 89

The one’s digit of the cube of 23 is ______.

• 6

• 7

• 3

• 9

Exercise | Q 8 | Page 89

A square board has an area of 144 square units. How long is each side of the board?

• 11 units

• 12 units

• 13 units

• 14 units

Exercise | Q 9 | Page 89

Which letter best represents the location of sqrt(25) on a number line? • A

• B

• C

• D

Exercise | Q 10 | Page 89

If one member of a pythagorean triplet is 2m, then the other two members are ______.

• m, m2 + 1

• m2 + 1, m2 – 1

• m2, m2 – 1

• m2, m + 1

Exercise | Q 11 | Page 89

The sum of successive odd numbers 1, 3, 5, 7, 9, 11, 13 and 15 is ______.

• 81

• 64

• 49

• 36

Exercise | Q 12 | Page 89

The sum of first n odd natural numbers is ______.

• 2n + 1

• n2

• n2 – 1

• n2 + 1

Exercise | Q 13 | Page 89

Which of the following numbers is a perfect cube?

• 243

• 216

• 392

• 8640

Exercise | Q 14 | Page 89

The hypotenuse of a right triangle with its legs of lengths 3x × 4x is ______.

• 5x

• 7x

• 16x

• 25x

Exercise | Q 15 | Page 89

The next two numbers in the number pattern 1, 4, 9, 16, 25 ... are ______.

• 35, 48

• 36, 49

• 36, 48

• 35, 49

Exercise | Q 16 | Page 90

Which among 432, 672, 522, 592 would end with digit 1?

• 43

• 672

• 522

• 592

Exercise | Q 17 | Page 90

A perfect square can never have the following digit in its ones place ______.

• 1

• 8

• 0

• 6

Exercise | Q 18 | Page 90

Which of the following numbers is not a perfect cube?

• 216

• 567

• 125

• 343

Exercise | Q 19 | Page 90

root(3)(1000) is equal to ______.

• 10

• 100

• 1

• None of these

Exercise | Q 20 | Page 90

If m is the square of a natural number n, then n is ______.

• The square of m

• Greater than m

• Equal to m

• sqrt(m)

Exercise | Q 21 | Page 90

A perfect square number having n digits where n is even will have square root with ______.

• n + 1 digit

• n/2 digit

• n/3 digit

• (n + 1)/2 digit

Exercise | Q 22 | Page 90

If m is the cube root of n, then n is ______.

• m3

• sqrt(m)

• m/3

• root(3)(m)

Exercise | Q 23 | Page 90

The value of sqrt(248 + sqrt(52 + sqrt(144) is ______.

• 14

• 12

• 16

• 13

Exercise | Q 24 | Page 90

Given that sqrt(4096) = 64, the value of sqrt(4096) + sqrt(40.96) is ______.

• 74

• 60.4

• 64.4

• 70.4

#### Fill in the blanks:

Exercise | Q 25 | Page 90

There are ______ perfect squares between 1 and 100.

Exercise | Q 26 | Page 90

There are ______ perfect cubes between 1 and 1000.

Exercise | Q 27 | Page 90

The units digit in the square of 1294 is ______.

Exercise | Q 28 | Page 91

The square of 500 will have ______ zeroes.

Exercise | Q 29 | Page 91

There are ______ natural numbers between n2 and (n + 1)2

Exercise | Q 30 | Page 91

The square root of 24025 will have ______ digits.

Exercise | Q 31 | Page 91

The square of 5.5 is ______.

Exercise | Q 32 | Page 91

The square root of 5.3 × 5.3 is ______.

Exercise | Q 33 | Page 91

The cube of 100 will have ______ zeroes.

Exercise | Q 34 | Page 91

1m2 = ______ cm2.

Exercise | Q 35 | Page 91

1m3 = ______ cm3.

Exercise | Q 36 | Page 91

One's digit in the cube of 38 is ______.

Exercise | Q 37 | Page 91

The square of 0.7 is ______.

Exercise | Q 38 | Page 91

The sum of first six odd natural numbers is ______.

Exercise | Q 39 | Page 91

The digit at the ones place of 572 is ______.

Exercise | Q 40 | Page 91

The sides of a right triangle whose hypotenuse is 17 cm are ______ and ______.

Exercise | Q 41 | Page 91

sqrt(1.96) = ______.

Exercise | Q 42 | Page 91

(1.2)3 = ______.

Exercise | Q 43 | Page 91

The cube of an odd number is always an ______ number.

Exercise | Q 44 | Page 91

The cube root of a number x is denoted by ______.

Exercise | Q 45 | Page 91

The least number by which 125 be multiplied to make it a perfect square is ______.

Exercise | Q 46 | Page 91

The least number by which 72 be multiplied to make it a perfect cube is ______.

Exercise | Q 47 | Page 91

The least number by which 72 be divided to make it a perfect cube is ______.

Exercise | Q 48 | Page 91

Cube of a number ending in 7 will end in the digit ______.

#### State whether the following statement is True or False:

Exercise | Q 49 | Page 91

The square of 86 will have 6 at the units place.

• True

• False

Exercise | Q 50 | Page 91

The sum of two perfect squares is a perfect square.

• True

• False

Exercise | Q 51 | Page 91

The product of two perfect squares is a perfect square.

• True

• False

Exercise | Q 52 | Page 91

There is no square number between 50 and 60.

• True

• False

Exercise | Q 53 | Page 92

The square root of 1521 is 31.

• True

• False

Exercise | Q 54 | Page 92

Each prime factor appears 3 times in its cube.

• True

• False

Exercise | Q 55 | Page 92

The square of 2.8 is 78.4.

• True

• False

Exercise | Q 56 | Page 92

The cube of 0.4 is 0.064

• True

• False

Exercise | Q 57 | Page 92

The square root of 0.9 is 0.3.

• True

• False

Exercise | Q 58 | Page 92

The square of every natural number is always greater than the number itself.

• True

• False

Exercise | Q 59 | Page 92

The cube root of 8000 is 200.

• True

• False

Exercise | Q 60 | Page 92

There are five perfect cubes between 1 and 100.

• True

• False

Exercise | Q 61 | Page 92

There are 200 natural numbers between 1002 and 1012.

• True

• False

Exercise | Q 62 | Page 92

The sum of first n odd natural numbers is n2.

• True

• False

Exercise | Q 63 | Page 92

1000 is a perfect square.

• True

• False

Exercise | Q 64 | Page 92

A perfect square can have 8 as its units digit.

• True

• False

Exercise | Q 65 | Page 92

For every natural number m, (2m –1, 2m2 –2m, 2m2 –2m + 1) is a pythagorean triplet.

• True

• False

Exercise | Q 66 | Page 92

All numbers of a pythagorean triplet are odd.

• True

• False

Exercise | Q 67 | Page 92

For an integer a, a3 is always greater than a2.

• True

• False

Exercise | Q 68 | Page 92

If x and y are integers such that x2 > y2, then x3 > y3.

• True

• False

Exercise | Q 69 | Page 92

Let x and y be natural numbers. If x divides y, then x3 divides y3.

• True

• False

Exercise | Q 70 | Page 92

If a2 ends in 5, then a3 ends in 25.

• True

• False

Exercise | Q 71 | Page 92

If a2 ends in 9, then a3 ends in 7.

• True

• False

Exercise | Q 72 | Page 92

The square root of a perfect square of n digits will have ((n + 1)/2) digits, if n is odd.

• True

• False

Exercise | Q 73 | Page 92

Square root of a number x is denoted by sqrt(x).

• True

• False

Exercise | Q 74 | Page 92

A number having 7 at its ones place will have 3 at the units place of its square.

• True

• False

Exercise | Q 75 | Page 93

A number having 7 at its ones place will have 3 at the ones place of its cube.

• True

• False

Exercise | Q 76 | Page 93

The cube of a one-digit number cannot be a two-digit number.

• True

• False

Exercise | Q 77 | Page 93

Cube of an even number is odd.

• True

• False

Exercise | Q 78 | Page 93

Cube of an odd number is even.

• True

• False

Exercise | Q 79 | Page 93

Cube of an even number is even.

• True

• False

Exercise | Q 80 | Page 93

Cube of an odd number is odd.

• True

• False

Exercise | Q 81 | Page 93

999 is a perfect cube.

• True

• False

Exercise | Q 82 | Page 93

363 × 81 is a perfect cube.

• True

• False

Exercise | Q 83 | Page 93

Cube roots of 8 are + 2 and – 2.

• True

• False

Exercise | Q 84 | Page 93

root(3)(8 + 27) = root(3)(8) + root(3)(27).

• True

• False

Exercise | Q 85 | Page 93

There is no cube root of a negative integer.

• True

• False

Exercise | Q 86 | Page 93

Square of a number is positive, so the cube of that number will also be positive.

• True

• False

#### Solve the following:

Exercise | Q 87 | Page 93

Write the first five square numbers.

Exercise | Q 88 | Page 93

Write cubes of first three multiples of 3.

Exercise | Q 89 | Page 93

Show that 500 is not a perfect square.

Exercise | Q 90 | Page 93

Express 81 as the sum of first nine consecutive odd numbers.

Exercise | Q 91.(a) | Page 93

Using prime factorisation, find which of the following are perfect squares.

484

Exercise | Q 91.(b) | Page 93

Using prime factorisation, find which of the following are perfect squares.

11250

Exercise | Q 91.(c) | Page 93

Using prime factorisation, find which of the following are perfect squares.

841

Exercise | Q 91.(d) | Page 93

Using prime factorisation, find which of the following are perfect squares.

729

Exercise | Q 92.(a) | Page 93

Using prime factorisation, find which of the following are perfect cubes

128

Exercise | Q 92.(b) | Page 93

Using prime factorisation, find which of the following are perfect cubes

343

Exercise | Q 92.(c) | Page 93

Using prime factorisation, find which of the following are perfect cubes

729

Exercise | Q 92.(d) | Page 93

Using prime factorisation, find which of the following are perfect cubes

1331

Exercise | Q 93.(a) | Page 93

Using distributive law, find the squares of 101

Exercise | Q 93.(b) | Page 93

Using distributive law, find the squares of  72

Exercise | Q 94 | Page 93

Can a right triangle with sides 6 cm, 10 cm and 8 cm be formed? Give reason.

Exercise | Q 95 | Page 93

Write the Pythagorean triplet whose one of the numbers is 4.

Exercise | Q 96.(a) | Page 94

Using prime factorisation, find the square roots of 11025

Exercise | Q 96.(b) | Page 94

Using prime factorisation, find the square roots of 4761

Exercise | Q 97.(a) | Page 94

Using prime factorisation, find the cube roots of 512

Exercise | Q 97.(b) | Page 94

Using prime factorisation, find the cube roots of 2197

Exercise | Q 98 | Page 94

Is 176 a perfect square? If not, find the smallest number by which it should be multiplied to get a perfect square.

Exercise | Q 99 | Page 94

Is 9720 a perfect cube? If not, find the smallest number by which it should be divided to get a perfect cube.

Exercise | Q 100 | Page 94

Write two Pythagorean triplets each having one of the numbers as 5.

Exercise | Q 101 | Page 94

By what smallest number should 216 be divided so that the quotient is a perfect square. Also find the square root of the quotient.

Exercise | Q 102 | Page 94

By what smallest number should 3600 be multiplied so that the quotient is a perfect cube. Also find the cube root of the quotient.

Exercise | Q 103.(a) | Page 94

Find the square root of the following by long division method.

1369

Exercise | Q 103.(b) | Page 94

Find the square root of the following by long division method.

5625

Exercise | Q 104.(a) | Page 94

Find the square root of the following by long division method.

27.04

Exercise | Q 104.(b) | Page 94

Find the square root of the following by long division method.

1.44

Exercise | Q 105 | Page 94

What is the least number that should be subtracted from 1385 to get a perfect square? Also find the square root of the perfect square.

Exercise | Q 106 | Page 94

What is the least number that should be added to 6200 to make it a perfect square?

Exercise | Q 107 | Page 94

Find the least number of four digits that is a perfect square

Exercise | Q 108 | Page 94

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

Exercise | Q 109 | Page 94

Find the least square number which is exactly divisible by 3, 4, 5, 6 and 8.

Exercise | Q 110 | Page 94

Find the length of the side of a square if the length of its diagonal is 10 cm.

Exercise | Q 111 | Page 94

A decimal number is multiplied by itself. If the product is 51.84, find the number.

Exercise | Q 112 | Page 94

Find the decimal fraction which when multiplied by itself gives 84.64

Exercise | Q 113 | Page 95

A farmer wants to plough his square field of side 150 m. How much area will he have to plough?

Exercise | Q 114 | Page 95

What will be the number of unit squares on each side of a square graph paper if the total number of unit squares is 256?

Exercise | Q 115 | Page 95

If one side of a cube is 15 m in length, find its volume.

Exercise | Q 116 | Page 95

The dimensions of a rectangular field are 80m and 18m. Find the length of its diagonal.

Exercise | Q 117 | Page 95

Find the area of a square field if its perimeter is 96m.

Exercise | Q 118 | Page 95

Find the length of each side of a cube if its volume is 512 cm3

Exercise | Q 119 | Page 95

Three numbers are in the ratio 1:2:3 and the sum of their cubes is 4500. Find the numbers.

Exercise | Q 120 | Page 95

How many square metres of carpet will be required for a square room of side 6.5 m to be carpeted.

Exercise | Q 121 | Page 95

Find the side of a square whose area is equal to the area of a rectangle with sides 6.4 m and 2.5 m.

Exercise | Q 122 | Page 95

Difference of two perfect cubes is 189. If the cube root of the smaller of the two numbers is 3, find the cube root of the larger number.

Exercise | Q 123 | Page 95

Find the number of plants in each row if 1024 plants are arranged so that number of plants in a row is the same as the number of rows.

Exercise | Q 124 | Page 95

A hall has a capacity of 2704 seats. If the number of rows is equal to the number of seats in each row, then find the number of seats in each row

Exercise | Q 125 | Page 95

A General wishes to draw up his 7500 soldiers in the form of a square. After arranging, he found out that some of them are left out. How many soldiers were left out?

Exercise | Q 126 | Page 95

8649 students were sitting in a lecture room in such a manner that there were as many students in the row as there were rows in the lecture room. How many students were there in each row of the lecture room?

Exercise | Q 127 | Page 95

Rahul walks 12 m north from his house and turns west to walk 35 m to reach his friend’s house. While returning, he walks diagonally from his friend’s house to reach back to his house. What distance did he walk while returning?

Exercise | Q 128 | Page 96

A 5.5m long ladder is leaned against a wall. The ladder reaches the wall to a height of 4.4m. Find the distance between the wall and the foot of the ladder.

Exercise | Q 129 | Page 96

A king wanted to reward his advisor, a wise man of the kingdom. So he asked the wiseman to name his own reward. The wiseman thanked the king but said that he would ask only for some gold coins each day for a month. The coins were to be counted out in a pattern of one coin for the first day, 3 coins for the second day, 5 coins for the third day and so on for 30 days. Without making calculations, find how many coins will the advisor get in that month?

Exercise | Q 130 | Page 96

Find three numbers in the ratio 2:3:5, the sum of whose squares is 608.

Exercise | Q 131 | Page 96

Find the smallest square number divisible by each one of the numbers 8, 9 and 10.

Exercise | Q 132 | Page 96

The area of a square plot is 101 1/400 m2. Find the length of one side of the plot.

Exercise | Q 133 | Page 96

Find the square root of 324 by the method of repeated subtraction.

Exercise | Q 134 | Page 96

Three numbers are in the ratio 2:3:4. The sum of their cubes is 0.334125. Find the numbers.

Exercise | Q 135 | Page 96

Evaluate: root(3)(27) + root(3)(0.008) + root(3)(0.064)

Exercise | Q 136 | Page 96

{(5^2 + (12^2)^(1/2))}^3

Exercise | Q 137 | Page 96

{(6^2 + (8^2)^(1/2))}^3

Exercise | Q 138 | Page 96

A perfect square number has four digits, none of which is zero. The digits from left to right have values that are: even, even, odd, even. Find the number.

Exercise | Q 139 | Page 96

Put three different numbers in the circles so that when you add the numbers at the end of each line you always get a perfect square. Exercise | Q 140 | Page 97

The perimeters of two squares are 40 and 96 metres respectively. Find the perimeter of another square equal in area to the sum of the first two squares.

Exercise | Q 141 | Page 97

A three-digit perfect square is such that if it is viewed upside down, the number seen is also a perfect square. What is the number?

Exercise | Q 142 | Page 97

13 and 31 is a strange pair of numbers such that their squares 169 and 961 are also mirror images of each other. Find two more such pairs.

## Chapter 3: Square-Square Root and Cube-Cube Root

Exercise ## NCERT solutions for Mathematics Exemplar Class 8 chapter 3 - Square-Square Root and Cube-Cube Root

NCERT solutions for Mathematics Exemplar Class 8 chapter 3 (Square-Square Root and Cube-Cube Root) 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 Exemplar Class 8 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics Exemplar Class 8 chapter 3 Square-Square Root and Cube-Cube Root are Properties of Square Numbers, Some More Interesting Patterns of Square Number, Square Root of Decimal Numbers, Concept of Square Number, Finding the Square of a Number, Concept of Square Roots, Finding Square Root Through Repeated Subtraction, Finding Square Root Through Prime Factorisation, Finding Square Root by Division Method, Estimating Square Root, Some Interesting Patterns of Cube Numbers, Concept of Cube Number, Concept of Cube Root, Cube Root Through Prime Factorisation Method, Finding the Cube Roots of the Cubic Numbers Through the Estimation Method.

Using NCERT Class 8 solutions Square-Square Root and Cube-Cube Root 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 NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 8 prefer NCERT Textbook Solutions to score more in exam.

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