How do you rationalise the denominator?

If a denominator is has just one square root (i.e 1/(3)^0.5). Then, since it is a fraction you can multiply top and bottom by the same number and maintain the value of the fraction. Hence we multiply top and bottom by the square root in the denominator,(in previous example we would use (3)^0.5). Then using the rules of roots we now have a rational denominator. If denominator has more than 1 part to it (i.e 1/(1+(5)^0.5)) then we must be more clever. Recall difference of 2 squares, (x+y)(x-y)=x^2-y^2, hence if either x or y were square roots then, the answer would be rational. So now consider1/((1+(5)^0.5) is the denominator, by multiplying top and bottom by (1-(5)^0.5) we have rationalised the denominator since we get (1-(5)^0.5)/(1-5)= (1-(5)^0.5)/(-4)