Question

Find the smallest number by which 21675 should be divided to make it a perfect square .

Answer 1

Factors of 21675 =
1, 3, 5, 15, 17, 25, 51, 75, 85, 255, 289, 425, 867, 1275, 1445, 4335, 7225.

in this given factors 25 and 289 are the perfect squares.

21675 = 25 x 289 x 3

when 21675 ÷ 3 , we get 7225.
7225 is a perfect square.
√7225 = 85.

.˙. Smallest number to which 21675 should divide to get perfect square = 3