Question

Find the smallest number by which 10368 be divided so that the result is a perfect square. Also, find the square root of the resulting numbers.

Answer 1

$10368=2\times 2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3\times 3$

On grouping the prime factors of 10368; one factor i.e. 2 is left which cannot be paired with equal factor.

$\therefore$ The given number should be divided by 2

Now, $\sqrt{\frac{10368}{2}}=\sqrt{\frac{2\times 2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3\times 3}{2}}$

$=2\times 2\times 2\times 3\times 3$

$=72$