# Thread: How do you rationalise when you have 3 surds in the denominator?

1. ## How do you rationalise when you have 3 surds in the denominator?

Can someone show me exactly step by step how to rationalise the denominator in this question?

$\frac{1}{\sqrt{2} + \sqrt{3} + \sqrt{5}}$

2. Originally Posted by MingMing
Can someone show me exactly step by step how to rationalise the denominator in this question?

$\frac{1}{\sqrt{2} + \sqrt{3} + \sqrt{5}}$
You have to doe this question in (at least) 2 steps:

$\dfrac{1}{\sqrt{2} + \sqrt{3} + \sqrt{5}}\cdot \dfrac{(\sqrt{2} + \sqrt{3})- \sqrt{5}}{(\sqrt{2} + \sqrt{3})- \sqrt{5}}=\dfrac{\sqrt{2} + \sqrt{3} - \sqrt{5}}{2\sqrt{6}}$

I'll leave the 2nd step for you.

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