Rationalizing Denominators with Radicals

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 Rationalization

Multiplies the numerator and denominator by Radical.

Rationalizing Operations

Rationalizing Operations

Rationalizing Operations

Rationalizing Solution

2 Rationalization of the type Rationalization Type

Multiplies numerator and denominator by Radical.

Radical Operations

Radical Operations

3 Rationalization of the type Rationalization TypeMultiply 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:

Conjugate of a Binomial

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

Sum by Difference

Rationalizing Operations

Rationalizing Operations

Rationalizing Operations

Rationalizing Operations

Rationalizing Operations

Rationalizing Solution