Nice :)
Here are a couple of examples (a denominator with a surd in it is irrational)
$$\frac{1}{\sqrt{5}} = \frac{1}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} = \frac{\sqrt{5}}{5} = 5$$ (we can do this because sqrt5/sqrt5 = 1)
Using Rosla's example:
1/(√5 -√6) x (√5 + √6)/(√5+√6) ([√5+√6] is the conjugate of [√5 -√6])
(√5 + √6)/(√5 -√6)(√5+√6)
(√5 + √6)/(√5^2 - √6^2) (as Rosala said we can do this beacuse (a-b)(a+b) = a^2 - b^2, meaning all the surds in the denominator are cancelled out)
(√5 + √6)/(5 - 6)
(√5 + √6)/-1 or
-(√5 + √6)/1 or
-√5 -√6
+980 
