# 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.

### Example No. 1

$\displaystyle\frac{2}{3\sqrt{3}}=\frac{2}{3\sqrt{3}}\cdot \frac{\sqrt{3}}{\sqrt{3}}=\frac{2\sqrt{3}}{\large{9}}$

### Example No. 2

$\displaystyle\frac{2}{2-\sqrt{3}}=\frac{2}{2-\sqrt{3}}\cdot \frac{2+\sqrt{3}}{2+\sqrt{3}}=\frac{2(2+\sqrt{3})}{2^2-\sqrt{3^2}}={2(2+\sqrt{3})}$

### Example No. 3

$\displaystyle\frac{1}{\sqrt{5}+\sqrt{3}}=\frac{1}{\sqrt{5}+\sqrt{3}}\cdot \frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}-\sqrt{3}}=\frac{\sqrt{5}-\sqrt{3}}{\large{2}}$

How you can see above, removing root isn't very hard process. Everything that we need is right multiplier, which can remove root.

2019-03-02

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