Question

If $\sqrt{10}=3.162$ then find the value of $\frac{1}{\sqrt{10}}$.

Answer 1

Calculate the required value.

Rationalize the given expression as follows.

$$\begin{gathered} \frac{1}{\sqrt{10}}=\frac{1}{\sqrt{10}}\times \frac{\sqrt{10}}{\sqrt{10}} \\ \Rightarrow \frac{1}{\sqrt{10}}=\frac{\sqrt{10}}{10} \end{gathered}$$

Since, $\sqrt{10}=3.162$

$$\begin{gathered} \Rightarrow \frac{1}{\sqrt{10}}=\frac{3.162}{10} \\ \Rightarrow \frac{1}{\sqrt{10}}=0.3162 \end{gathered}$$

Hence, the values of $\frac{1}{\sqrt{10}}$ is $0.3162$.