If the denominator is a single surd, multiply the numerator and denominator by the same surd
If the denominator is a binomial with a surd, multiply by the conjugate of the denominator
Use the identity ((a+b)(a-b)=a^2-b^2) to remove the surd from the denominator
Simplify the resulting fraction
Cancel any common factors if possible
If the denominator contains more than one surd term, choose a factor that makes the denominator a rational expression when expanded
Expand and simplify until no surds remain in the denominator