Question

Express each one of the following with rational denominator:

$\frac{14}{\sqrt{98}}$

Answer 1

Rationalize the denominator and simplify it.

The given irrational number is:

$\frac{14}{\sqrt{98}}=14\times \frac{1}{\sqrt{98}}$

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 $\frac{1}{\sqrt{98}}$, we multiply this by $\frac{\sqrt{98}}{\sqrt{98}}$.

$\begin{array}{c}\frac{14}{\sqrt{98}}=\frac{14}{\sqrt{98}}\times \frac{\sqrt{98}}{\sqrt{98}}\\ =\frac{14}{98}\times \sqrt{98}\\ =\frac{1}{7}\times \sqrt{49\times 2}\\ =\frac{1}{7}\times 7\sqrt{2}\\ =\sqrt{2}\end{array}$

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