Question

For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square number. Also, find the square root of the square number obtained.

(i) $252$ (ii) $2925$ (iii) $396$ (iv) $2645$ (v) $2800$ (vi) $1620$

Answer 1

i)

$252=\underset{–}{2\times 2}\times \underset{–}{3\times 3}\times 7$

Therefore, we need to divide $252$ by $7$ in order to make it a perfect square.

So, $\frac{252}{7}=36$

$\therefore \sqrt{36}=6$

ii)

$2925=\underset{–}{3\times 3}\times \underset{–}{5\times 5}\times 13$

Therefore, we need to divide $2925$ by $13$ in order to make it a perfect square.

So, $\frac{2925}{13}=225$

$\therefore \sqrt{225}=15$

iii)

$396=\underset{–}{2\times 2}\times \underset{–}{3\times 3}\times 11$

Therefore, we need to divide $396$ by $11$ in order to make it a perfect square.

So, $\frac{396}{11}=36$

$\therefore \sqrt{36}=6$

iv)

$2645=\underset{–}{23\times 23}\times 5$

Therefore, we need to divide $2645$ by $5$ in order to make it a perfect square.

So, $\frac{2645}{5}=529$

$\therefore \sqrt{529}=23$

v)

$2800=\underset{–}{2\times 2}\times \underset{–}{2\times 2}\times \underset{–}{5\times 5}\times 7$

Therefore, we need to divide $2800$ by $7$ in order to make it a perfect square.

So, $\frac{2800}{7}=400$

$\therefore \sqrt{400}=20$

vi)

$1620=\underset{–}{2\times 2}\times \underset{–}{3\times 3}\times \underset{–}{3\times 3}\times 5$

Therefore, we need to divide $1620$ by $5$ in order to make it a perfect square.

So, $\frac{1620}{5}=324$

$\therefore \sqrt{324}=18$