# simplifying surd

• April 10th 2006, 11:37 AM
macca101
simplifying surd
Think I'm missing something really fundamental here why does

$
\frac{16+\sqrt 32}{2}
$

Simplify to

$
8+\sqrt 8
$

and not

$
8+\sqrt 16
$

and what rules or hints can you give to help simplify surd's in general
• April 10th 2006, 11:41 AM
ThePerfectHacker
Quote:

Originally Posted by macca101
Think I'm missing something really fundamental here why does

$
\frac{16+\sqrt 32}{2}
$

Simplify to

$
8+\sqrt 8
$

and not

$
8+\sqrt 16
$

and what rules or hints can you give to help simplify surd's in general

Because $\frac{\sqrt{32}}{2}\not =\sqrt{16}$, rather,
$\frac{\sqrt{32}}{2}=\frac{\sqrt{4\cdot 8}}{2}=\frac{2\sqrt{8}}{2}=\sqrt{8}$
Thus,
$\frac{16+\sqrt{32}}{2}=8+\sqrt{8}$
You can still simplify it further.