Question

Check whether $1152$ is a perfect square. If not, then find the least number by which it should be divided so that, the quotient becomes a perfect square. Also, find the square root of the quotient.

• A. $2;24$
• B. $3;24$
• C. $2;19$
• D. $3;19$

Answer 1

The correct option is A $2;24$

$1152=\underset{–}{2\times 2}\times \underset{–}{2\times 2}\times \underset{–}{2\times 2}\times 2\times \underset{–}{3\times 3}$
All the prime factors except $2$ can be paired.

Thus $1152$ is not a perfect square
Thus, we should divide $1152$ by $2$ to get the perfect square.
$1152÷2=576$
$576=\underset{–}{2\times 2}\times \underset{–}{2\times 2}\times \underset{–}{2\times 2}\times \underset{–}{3\times 3}$
Thus, the required least number is $2and\sqrt{576}=24$.