Question

By what smallest number should $216$ be divided so that the quotient is a perfect square. Also find the square root of the quotient.

Answer 1

Let us first determine the factors by the method of prime factorization,

Factors of $216=2\times 2\times 2\times 3\times 3\times 3$

On grouping and pairing the obtained factors we get $=\left(2\times 2\right)\times 2\times \left(3\times 3\right)\times 3$

Factors $2$ and $3$ has no pair.

∴$216$ is not a perfect square.

The smallest number it should be divided to get a perfect square is .$3\times 2=6$

Then,

$$\begin{gathered} =216÷6 \\ =36 \end{gathered}$$

Factors of $36=6\times 6$

$\begin{array}{rcl}\sqrt{36}& =& \sqrt{6\times 6}\\ & =& \sqrt{6^2}\\ & =& 6\end{array}$

∴$36$ is a perfect square

$6$ is the square root of $36$.

Hence, $216$ should be divide by $6$ to get quotient as perfect square .