Question

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

(i) 252                (ii) 2925

Answer 1

(i) 252 can be factorised as follows.

2	252
2	126
3	63
3	21
7	7
	1

252 = 2 x 2 x 3 x 3 x 7

Here, prime factor 7 does not have its pair, If we divide this number by 7, then the number will become a perfect square. Therefore, 252 has to be divided by 7 to obtain a perfect square.

252 ÷7 = 36 is a perfect square.

36 = 2 x 2 x 3 x 3

∴ √36 = 2 x 3 = 6

(ii) 2925 can be factorised as follows.

3	2925
3	975
5	325
5	65
13	13
	1

2925 = 3 x 3 x 5 x 5 x 13

Here, prime factor 13 does not have its pair. If we divide this number by 13, then the number will become a perfect square. Therefore, 2925 has to be divided by 13 to obtain a perfect square.

2925 ÷13 = 225 is a perfect square.

225 = 3 x 3 x 5 x 5

∴ √225 = 3 x 5 = 15