# NCERT Class 8 Mathematics Solutions: Chapter 6 – Squares and Square Roots Exercise 6.3 Part 4 (For CBSE, ICSE, IAS, NET, NRA 2022)

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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

(i) 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

 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

 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

 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

 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

 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.

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