Question

What is the square root of $72$?

Answer 1

Determine the square root of $72$.

The square root of a number is the value that returns the original number when multiplied by itself.

Find the prime factors of $72$:

$72=2\times 2\times 2\times 3\times 3$

Take square root from both sides of the above equation:

$$\begin{gathered} \sqrt{72}=\sqrt{2\times 2\times 2\times 3\times 3} \\ \Rightarrow \sqrt{72}=2\times 3\times \sqrt{2} \\ \Rightarrow \sqrt{72}=6\times \sqrt{2}(\because \sqrt{2}=1.414) \\ \Rightarrow \sqrt{72}=6\times 1.414 \\ \Rightarrow \sqrt{72}=8.4852 \end{gathered}$$

Hence, the square root of $72$ is $8.4852$.