Question

Express each one of the following with rational denominator:

$\frac{2}{\sqrt{7}}$

Answer 1

Rationalize the denominator

Given irrational numbers is:

$\frac{2}{\sqrt{7}}$

The numbers which can be expressed in the form of $\frac{p}{q}$ where both $p$ and $q$ are integers and $q\ne 0$ is known as rational numbers.

To rationalize the denominator of $\frac{1}{\sqrt{7}}$, we multiply this by $\frac{\sqrt{7}}{\sqrt{7}}$.

$\begin{array}{c}\frac{2}{\sqrt{7}}=\frac{2}{\sqrt{7}}\times \frac{\sqrt{7}}{\sqrt{7}}\\ =\frac{2}{7}\sqrt{7}\end{array}$

Hence, the given number can be expressed as $\frac{2}{7}\sqrt{7}$.