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 
, 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 difference of squares".
