# Rationalise

• February 3rd 2011, 04:27 AM
Monster32432421
Rationalise
Rationalise
http://img80.imageshack.us/img80/2046/333sco.jpg
Could someone show most of the main steps in achieving the rationalised result of http://img638.imageshack.us/img638/323/24275821.jpg
I tried many methods and failed.
thank you
• February 3rd 2011, 04:38 AM
e^(i*pi)
Did you multiply top and bottom by the conjugate of the denominator?

$\dfrac{(2-\sqrt{2})-\sqrt{3}}{(2+\sqrt{2})-\sqrt{3}} \cdot \dfrac{(2+\sqrt{2})+\sqrt{3}}{(2+\sqrt{2})+\sqrt{3 }} = \dfrac{(4-2)+ (2-\sqrt{2})\sqrt{3} - (2+\sqrt{2})\sqrt{3}-3}{4 + 2\sqrt{2}+2-3}$

$= \dfrac{2\sqrt{3}-\sqrt{6}-2\sqrt{3}+\sqrt{6}-1}{3+2\sqrt{2}} = -\dfrac{1}{3+2\sqrt{2}}$

You should be able to multiply by $\dfrac{3-2\sqrt{2}}{3-2\sqrt{2}}$ to rationalise