# Rationalization of Denominators

**To rationalize a radical, remove the radicals from the denominator**. This allows fractions with radicals to be added, subtracted, multiplied and divided in a much simpler manner.

Three cases can be distinguished.

1** Rationalization** of the type

**Multiply the numerator and denominator by **.

2** Rationalization** of the type

**Multiply the numerator and denominator by **.

3** Rationalization** of the type , and in general when the denominator is a binomial with at least one radical**. **

Multiply the numerator and denominator by the conjugate of the denominator.

The conjugate of a binomial is equal to the binomial with the central sign changed:

Also, bear in mind that: "**sum by difference is equal to the difference of squares**".

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