Question

The factorization of a number is $2\times 2\times 6\times 9\times 24.$ Is this number a perfect square? Answer in Yes/ No.

Answer 1

The given number is $2\times 2\times 6\times 9\times 24.$

The prime factorization of the number is $2\times 2\times (2\times 3)\times (3\times 3)\times (2\times 2\times 2\times 3)$
$=2^6\times 3^4$
$=(2^3{)}^2\times (3^2{)}^2$
$=(2^3\times 3^2{)}^2={72}^2$

As the given number can be expressed as square of another number, it is a perfect square.