Question

How do you simplify $\sqrt{216n}$?

Answer 1

Hint: First try to write the constant ‘216’ in terms of the multiplication of its prime factors along with the variable ‘n’ inside the radical function itself. From the radical take each pair of factors only once to obtain the square root and keep the remaining factors inside the radical only.

Complete step by step answer:
Considering the expression we have $\sqrt{216n}$
To find the square root first we have to express ‘216’ in terms of the multiplication of its prime factors.
So, ‘216’ can be written as $216=2\times 2\times 2\times 3\times 3\times 3$
Now, the given expression becomes
 $\sqrt{216n}=\sqrt{2\times 2\times 2\times 3\times 3\times 3\times n}$
We can say that there is one pair of ‘2’ and one pair of ‘3’, so taking one ‘2’ and one ‘3’ from each pair and keeping the rest inside the radical we can obtain the square root as
$\begin{align}
  & \sqrt{2\times 2\times 2\times 3\times 3\times 3\times n} \\
 & =2\times 3\times \sqrt{2\times 3\times n} \\
 & =6\sqrt{6n} \\
\end{align}$
Hence, the value of the given expression $\sqrt{216n}=6\sqrt{6n}$
This is the required solution of the given question.

Note:
Constant should be written in terms of the multiplication of prime factors. For the square root from each pair of factors only one factor should be taken and the remaining factors should be kept inside the radical. Necessary calculations and simplifications should be done.