Find the value to three places of decimals of each of the following. It is given that$ \sqrt{2}=1.414, \sqrt{3}=1.732, \sqrt{5}=2.236 $ and $ \sqrt{10}=3.162 $.
$ \frac{2}{\sqrt{3}} $

Given:

\( \sqrt{2}=1.414, \sqrt{3}=1.732, \sqrt{5}=2.236 \) and \( \sqrt{10}=3.162 \).

To do: 

We have to find the value of \( \frac{2}{\sqrt{3}} \) to three decimal places.

Solution:

We know that,

Rationalising factor of a fraction with denominator ${\sqrt{a}}$ is ${\sqrt{a}}$.

Rationalising factor of a fraction with denominator ${\sqrt{a}-\sqrt{b}}$ is ${\sqrt{a}+\sqrt{b}}$.

Rationalising factor of a fraction with denominator ${\sqrt{a}+\sqrt{b}}$ is ${\sqrt{a}-\sqrt{b}}$.

Therefore,

$\frac{2}{\sqrt{3}}=\frac{2 \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}}$

$=\frac{2 \sqrt{3}}{3}$

$=\frac{2 \times 1.732}{3}$

$=\frac{3.464}{3}$

$=1.154$

Hence, $\frac{\sqrt{2}}{\sqrt{3}}=1.154$. 

Tutorialspoint

Updated on: 10-Oct-2022

126 Views

Kickstart Your Career

Get certified by completing the course

Get Started