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
Multiplies the numerator and denominator by .
2 Rationalization of the type
Multiplies numerator and denominator by .
3 Rationalization of the type 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 difference of squares".