Question

How do you simplify the square root of $72$?

Answer 1

Simplify the square root.

Given: $\sqrt{72}$

Factorize $72$

$\begin{array}{rcl}72& =& 12\times 6\\ & =& 4\times 3\times 2\times 3\\ & =& 2\times 2\times 3\times 2\times 3\\ & =& \left(2\times 2\right)\times \left(3\times 3\right)\times 2\\ & =& 2^2\times 3^2\times 2\end{array}$

Since we know that $\sqrt{72}$ can be written as, ${\left(72\right)}^{\frac{1}{2}}$

$\begin{array}{rcl}{\left(72\right)}^{\frac{1}{2}}& =& {\left(2^2\times 3^2\times 2\right)}^{\frac{1}{2}}\\ & =& {\left(2^2\right)}^{\frac{1}{2}}\times {\left(3^2\right)}^{\frac{1}{2}}\times {\left(2\right)}^{\frac{1}{2}}\\ & =& 2^{\frac{2}{2}}\times 3^{\frac{2}{2}}\times 2^{\frac{1}{2}}\\ & =& 2^1\times 3^1\times 2^{\frac{1}{2}}\\ & =& 6\sqrt{2}\end{array}$

Hence, the simplified form of $\sqrt{72}$ is $6\sqrt{2}$