Question

Find the smallest number by which 1152 must be divided so that it becomes a perfect square. Also, find the number whose square is the resulting number.

Answer 1

By factorization $1152=2\times 2\times 2\times 2\times 2\times 2\times 2\times 3\times 3$

Grouping the factors in pairs as $1152=2\times (2\times 2)\times (2\times 2)\times (2\times 2)\times (3\times 3)$, we see that one 2 is left unpaired
$\therefore$ Dividing 1152 by 2, we get the perfect square and square root of the resulting number $\frac{1152}{2}=576$, will be $2\times 2\times 2\times 3=24$.