# Adding square roots (easy question)

• July 21st 2009, 08:03 PM
azurephantom
http://img32.imageshack.us/img32/945/howx.jpg

Can anyone explain to me what happened here?
I understand that the 2 on the bottom is cause the denominator has to be the same, but I don't understand what happened on top.
• July 21st 2009, 08:10 PM
Rapha
Hello.

Quote:

Originally Posted by azurephantom
http://img32.imageshack.us/img32/945/howx.jpg

Can anyone explain to me what happened here?
I understand that the 2 on the bottom is cause the denominator has to be the same, but I don't understand what happened on top.

$\sqrt{2} - 2 \sqrt{2} =1* \sqrt{2} - 2* \sqrt{2} = -1 \sqrt{2}$. because

$1* \sqrt{2} - 2* \sqrt{2} = (1-2)*\sqrt{2} = (-1)*\sqrt{2}$

After that you can add the remaining '2' to $(-1)*\sqrt{2}$, because all these terms have the same denominator!

This leads to - $1*\sqrt{2}+2 = -\sqrt{2}+2$ on the top

Yours
Rapha
• July 21st 2009, 08:11 PM
AlephZero
$\frac{\sqrt{2}}{2}-\frac{2\sqrt{2}}{2}+\frac{2}{2}$

$=\frac{\sqrt{2}-2\sqrt{2}+2}{2}=\frac{-\sqrt{2}+2}{2}.$