Question

Find the smallest number by which $252$ must be multiplied to get a perfect square. Also, find the square root of the perfect square so obtained.

• A. $8,48$
• B. $7,42$
• C. $9,42$
• D. $7,48$

Answer 1

The correct option is B $7,42$

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

The prime factor $7$ does not appear in pairs. To make $252$ a perfect square we need one more $7$.

Hence, the smallest number by which $252$ must be multiplied so that
the product is a perfect square is $7$.

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

$\sqrt{252\times 7}=\sqrt{\underset{–}{2\times 2}\times \underset{–}{3\times 3}\times \underset{–}{7\times 7}}=2\times 3\times 7=42$