1. ## Rationalise and Simplify

Guys,

I recently got a practice problem to try based on something or other I did a few years back in school. Thought I could handle it but apparently not:

Rationalise the denominator of, and thus simplify the expression

$\frac{2\sqrt{2}}{4-\sqrt{14}} -2\sqrt{7}$

Now I whats getting me is the 4 - root 14 in the denominator. If it were simply root 14 I would be able to rationalise and simplify no problem.

Thanks.

2. $\displaystyle \frac{2\sqrt{2}}{4-\sqrt{14}} -2\sqrt{7} = \left[\dfrac{2\sqrt{2}}{4-\sqrt{14}} \times \frac{4+\sqrt{14}}{4+\sqrt{14}}\right] -2\sqrt{7}$

simplify and finish.. Can you?

3. I got a bit further but hit another jam.

I got to

$\frac{4\sqrt{7}}{-14+4\sqrt{14}} -2\sqrt{7}$

4. No...

$\left[\dfrac{2\sqrt{2}}{4-\sqrt{14}} \times \dfrac{4+\sqrt{14}}{4+\sqrt{14}}\right]$

$= \dfrac{8\sqrt{2}+2\sqrt{28}}{16-14}$