Hi,
Could someone please show the steps that go to simplifying the below:
[SQRT(6) + 3*SQRT(2)] / [3+SQRT(5)]
Thanks, your help will be greatly appreciated.
Andy
$\dfrac{\sqrt{6}+3\sqrt{2}}{3+\sqrt{5}}=\dfrac{ \sqrt{6}+3\sqrt{2}}{3+\sqrt{5}}\cdot 1=$
$\dfrac{\sqrt{6}+3\sqrt{2}}{3+\sqrt{5}}\cdot \dfrac{3-\sqrt{5}}{3-\sqrt{5}}=$
$\dfrac{3\sqrt{6}+9\sqrt{2}-\sqrt{30}-3\sqrt{10}}{9-5}=$
$\dfrac{3\sqrt{6}+9\sqrt{2}-\sqrt{30}-3\sqrt{10}}{4}$
this form should be acceptable. You can tinker with it further to get
$\dfrac{3\sqrt{2}\sqrt{3}+9\sqrt{2}-\sqrt{2}\sqrt{3}\sqrt{5}-3\sqrt{2}\sqrt{5}}{4}=$
$\dfrac{\sqrt{2} \left(3\sqrt{3}+9-\sqrt{3} \sqrt{5}-3\sqrt{5}\right)}{4}=$
$\dfrac{\sqrt{2}\left(3+\sqrt{3}\right)\left(3-\sqrt{5}\right)}{4}$