NCERT Class 8 Mathematics Solutions: Chapter 6 – Squares and Square Roots Exercise 6.3 Part 4

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Image of Prime Factor of numbers

Image of Prime Factor of Numbers

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Question: 5 For each of the following numbers find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also, find the square root of the square number so obtained:

(i) 252

(ii) 180

(iii) 1008

(iv) 2028

(v) 1458

(vi) 768

Answer:

(i) 252

Find the Square Roots of 252

2

252

2

126

3

63

3

21

7

7

1

Here, prime factor 7 has no pair.

Therefore 252 must be multiplied by 7 to make it a perfect square.

(ii) 180

Find the Square Roots of 180

2

180

2

90

3

45

3

15

5

5

1

Here, prime factor 5 has no pair.

Therefore 180 must be multiplied by 5 to make it a perfect square.

(iii) 1008

Find the Square Roots of 1008

2

1008

2

504

2

252

2

126

3

63

3

21

7

7

1

Here, prime factor 7 has no pair.

Therefore 1008 must be multiplied by 7 to make it a perfect square.

(iv) 2028

Find the Square Roots of 2028

2

2028

2

1014

3

507

13

169

13

13

1

Here, prime factor 3 has no pair.

Therefore 2028 must be multiplied by 3 to make it a perfect square.

(v) 1458

Find the Square Roots of 1458

2

1458

3

729

3

243

3

81

3

27

3

9

3

3

1

Here, prime factor 2 has no pair.

Therefore 1458 must be multiplied by 3 to make it a perfect square.

(vi) 768

Find the Square Roots of 768

2

768

2

384

2

192

2

96

2

48

2

24

2

12

2

6

3

3

1

Here, prime factor 3 has no pair.

Therefore 768 must be multiplied by 3 to make it a perfect square.