Question

What is the square root of $160$?

Answer 1

Determine the square root of$160$.

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

Find the prime factors of $160$:

$160=2\times 2\times 2\times 5\times 2\times 2$

Take the square root from both sides of the above equation:

$$\begin{gathered} \sqrt{160}=\sqrt{2\times 2\times 2\times 5\times 2\times 2} \\ \Rightarrow \sqrt{160}=\sqrt{\underline{2\times 2}\times \underline{2\times 2}\times 2\times 5} \\ \Rightarrow \sqrt{160}=2\times 2\sqrt{2\times 5} \\ \Rightarrow \sqrt{160}=4\times \sqrt{2}\times \sqrt{5} \\ \Rightarrow \sqrt{160}=4\times 1.414\times 2.236 \\ \Rightarrow \sqrt{160}=4\times 3.161 \\ \Rightarrow \sqrt{160}=12.644 \end{gathered}$$

Hence, the square root of $160$ is $12.644$.