Question

What is the square root of $\frac{1}{3}$?

Answer 1

Determine the square root of$\frac{1}{3}$.

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

To find$\sqrt{\frac{1}{3}}$, we will proceed as given below:

$$\begin{gathered} \sqrt{\frac{1}{3}}=\frac{\sqrt{1}}{\sqrt{3}} \\ \Rightarrow \sqrt{\frac{1}{3}}=\frac{\sqrt{1}}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}\mathrm{rationalising}\mathrm{the}\mathrm{fraction} \\ \Rightarrow \sqrt{\frac{1}{3}}=\frac{\sqrt{1}\times \sqrt{3}}{3}(\because \surd 1=1and\surd 3=1.7302) \\ \Rightarrow \sqrt{\frac{1}{3}}=\frac{1\times 1.7302}{3} \\ \Rightarrow \sqrt{\frac{1}{3}}=0.577 \end{gathered}$$

Hence, the square root of $\frac{1}{3}$ is $0.577$.