Simplifying Surds

1. Sep 8, 2005

V-Tec

Ok here is my problem, I am not sure how to simplify surds with additions and subtractions in them such as ones like this:

http://img212.imageshack.us/img212/474/math010iz.gif [Broken]

At the moment I have managed to simplify it to this:

http://img212.imageshack.us/img212/2011/math026eg.gif [Broken]

However it is not simplified as possible, can someone give me some words of wisdom? Any help greatly appreciated!

Last edited by a moderator: May 2, 2017
2. Sep 8, 2005

EnumaElish

In this case, 80 = 4 x 20, so $\sqrt{80}=\sqrt 4 \times\sqrt {20}=2\sqrt {20}$.

Therefore $\sqrt{20}+\sqrt{80}= (1+2)\sqrt{20}=3\sqrt{20}$, which is $3\times 2\times\sqrt 5 = 6\sqrt 5$.