Question

Is $176$ a perfect square? If not, find the smallest number by which it should be multiplied to get a perfect square.

Answer 1

Check whether $176$is a perfect square or not?

Perfect square: A perfect square is a number that can be expressed as the product of an integer by itself.

Upon prime factorization $176$ we get

$$\begin{gathered} 176=2\times 2\times 2\times 2\times 11 \\ 176=(2\times 2)\times (2\times 2)\times 11 \end{gathered}$$

As we can see that $11$does not occur in pair.

Hence $176$ is not a perfect square and in order to make it a perfect square we must multiply it to $11$.