Question

How do I do this?

Answer 1

\[\frac{ \sqrt{6} }{ 4-\sqrt{6} }\]

Answer 2

First of all, you want the conjugate.

Answer 3

The conjugate if \(a+\sqrt{b}\) is \(a-\sqrt{b}\) and vice versa.

Answer 4

So we want the conjugate of \(4-\sqrt{6}\)

Answer 5

What do you think it would be?

Answer 6

Guess

Answer 7

4+ \[\sqrt{6}\] ?

Answer 8

Yes

Answer 9

Now multiply the top and bottom by the conjugate.

Answer 10

It turns out that: \((a+\sqrt b)(a-\sqrt b) = a^2-b\)

Answer 11

So we will get rid of square roots in the denominator at least.