# Removing irrationality from the fractions

In this article we will teach you how to remove irrationality from the fractions.

Removing irrationality from the fraction means that we must remove root from the denominator. To show you how to remove irrationality from the fractions, we will solve three different example tasks.

Remove the irrationality in the denominator $\frac{2}{3\sqrt{3}}$

$$\frac{2}{3\sqrt{3}}=\frac{2}{3\sqrt{3}}\cdot \frac{\sqrt{3}}{\sqrt{3}}=\frac{2\sqrt{3}}{9}$$Remove the irrationality in the denominator $\frac{2}{2-\sqrt{3}}$

$$\frac{2}{2-\sqrt{3}}=\frac{2}{2-\sqrt{3}}\cdot \frac{2+\sqrt{3}}{2+\sqrt{3}}=\frac{2(2+\sqrt{3})}{2^2-\sqrt{3^2}}={2(2+\sqrt{3})}$$Remove the irrationality in the denominator $\frac{1}{\sqrt{5}+\sqrt{3}}$

$$\frac{1}{\sqrt{5}+\sqrt{3}}=\frac{1}{\sqrt{5}+\sqrt{3}}\cdot \frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}-\sqrt{3}}=\frac{\sqrt{5}-\sqrt{3}}{2}$$How you can see above, removing root isn't very hard process. Everything that we need is right multiplier, which can remove root.

## Wanna check your skills?

A quiz is based on this article and has 5 questions.

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### Quiz

2019-03-02

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