Question

(i) Find the smallest number by which 2592 be multiplied so that the product is a perfect square.

(ii) Find the smallest number by which 12748 be multiplied so that the product is a perfect square ?

Answer 1

(i) $2592=\overline{2\times 2}\times \overline{2\times 2}\times 2\times \overline{3\times 3}\times \overline{3\times 3}$
On grouping the prime factors of 2592 as shown ; on factor i.e 2 is left which cannot be paired with equal factor.

$\therefore$ The given number should be multiplied by 2 to make the given number a perfect square.

(ii) $12748=\overline{2\times 2}\times 3187$
On grouping the prime factors of 12748 as shown ; on factor i.e 3187 is left which cannot be paired with equal factor.

$\therefore$ The given number should be multiplied by 3187