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 x 2 x 3 x 3 x 7
Here, prime factor 7 has no pair. Therefore 252 must be
multiplied by 7 to make it a perfect square.
∴ 252 x 7 = 1764
and √1764 = 2x3x7=42

(ii) 180 = 2 x 2 x 3 x 3 x 5
Here, prime factor 5 has no pair. Therefore 180 must be
multiplied by 5 to make it a perfect square.
∴ 180 x 5 = 900
and √900= 2x3x5=30

(iii) 1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7
Here, prime factor 7 has no pair. Therefore 1008 must be
multiplied by 7 to make it a perfect square.
∴ 1008 x 7 = 7056
and √7056 = 2x2x3x7 =84

(iv) 2028 = 2 x 2 x 3 x 13 x 13
Here, prime factor 3 has no pair. Therefore 2028 must be
multiplied by 3 to make it a perfect square.
∴ 2028 x 3 = 6084
And √6080 = √2x2x3x3x13x13 =78

(v) 1458 = 2 x 3 x 3 x 3 x 3 x 3 x 3
Here, prime factor 2 has no pair. Therefore 1458 must be
multiplied by 2 to make it a perfect square.
∴ 1458 x 2 = 2916
and √2916 = 2x3x3x3 = 54

(vi) 768 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3
Here, prime factor 3 has no pair. Therefore 768 must be
multiplied by 3 to make it a perfect square.
∴ 768 x 3 = 2304
and √2304 = 2x2x2x2x3 = 48

Class 8 Maths Chapter 6 Exercise 6.3 Solution in Video

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