Find the smallest number by which 1152 must be divided so that it becomes a perfect square.

The prime factorisation of 1152:

1152 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3

Grouping the factors into pairs of equal factors, we get:

1152 = (2 x 2) x (2 x 2) x (2 x 2) x (3 x 3) x 2

The factor, 2, at the end, does not have a pair. Therefore, we must divide 1152 by 2 to make a perfect square. The new number is:

(2 x 2) x (2 x 2) x (2 x 2) x (3 x 3) = 576

Taking one factor from each pair on the LHS, the square root of the new number is 2 x 2 x 2 x 3, which is equal to 24.