Simplifying fractions with surds.

**kensington** · October 16th 2010, 10:05 AM

Im doing my homework questions when i began to noticed my answers were different then those in the solutions book. I then realized that theysimplified it but i have no idea how it was done.

for example :

2/ Sqrt54 = sqrt6/9

How did they simplify 2/sqrt54 to sqrt6/9 and how do you know when to simplify further??

**Unknown008** · October 16th 2010, 10:14 AM

You can do like this:

$\dfrac{2}{\sqrt{54}}$

What is 54? 6 x 9, right?

$\dfrac{2}{\sqrt{54}} = \dfrac{2}{\sqrt{6\times 9}} = \dfrac{2}{\sqrt{6}\times \sqrt{9}} = \dfrac{2}{3\sqrt{6}}$

Now, multiply by $\dfrac{\sqrt6}{\sqrt6}$

$\dfrac{2}{3\sqrt{6}} \times \dfrac{\sqrt6}{\sqrt6}= \dfrac{2\sqrt{6}}{3\sqrt{6}\sqrt{6}} = \dfrac{2\sqrt6}{3\times6} = \dfrac{2\sqrt6}{18} = \dfrac{\sqrt6}{9}$

I hope it helps!

**kensington** · October 16th 2010, 10:15 AM

Thank u sooo much!

**Unknown008** · October 16th 2010, 10:17 AM

You're welcome

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