# Math Help - surds

1. ## surds

express $\frac{16+\frac{2\sqrt{18}}{2}}{2+\frac{6}{\sqrt{2} }} \divide 2$
in the form $a+b\sqrt{2}$ where a and b are integers

2. Originally Posted by Punch
express $\frac{16+\frac{2\sqrt{18}}{2}}{2+\frac{6}{\sqrt{2} }} \divide 2$
in the form $a+b\sqrt{2}$ where a and b are integers
You can start by simplifying the denominator.

Combine the fraction to get $\frac{2(\sqrt{2}+3)}{\sqrt{2}}$

Then simplify it and you are left with $2+3\sqrt{2}$

3. okay... i rationalised and am stucked @ $\frac{14-(\frac{84}{\sqrt{2}})}{-14}$

4. Yes, you're almost done, except that you did a mistake.

I got:

$\HUGE{\frac{14-\frac{42}{\sqrt{2}}}{-14}}$

Remember that:

$\frac{a+b}{c} = \frac{a}{c} + \frac{b}{c}$