1. ## Surds Help

Hey I'm having problems figuring out how to do this surd.

16/(√20+√12)

I know the answer is 4(√5-√3) but can you plz give me a step by step answer on how to do this...thanks.

2. Originally Posted by digideens
Hey I'm having problems figuring out how to do this surd.

16/(√20+√12)

I know the answer is 4(√5-√3) but can you plz give me a step by step answer on how to do this...thanks.
Multiply both top and bottom by $\sqrt{20}-\sqrt{12}$:

$
\frac{16}{\sqrt{20}+\sqrt{12}}=\frac{16(\sqrt{20}-\sqrt{12})}{(\sqrt{20}+\sqrt{12})(\sqrt{20}-\sqrt{12})}
$

$
=\frac{16(\sqrt{20}-\sqrt{12})}{20-12}=4(\sqrt{5}-\sqrt{3})
$

RonL

3. is there another step between the

=16(√20-√12)/20-12 and
= 4(√5-√3)

4. Originally Posted by digideens
is there another step between the

=16(√20-√12)/20-12 and
= 4(√5-√3)
Yes,
You have,
$\frac{16(\sqrt{20}-\sqrt{12})}{8}$
Simplyfy fraction to $2(\sqrt{20}-\sqrt{12})$
Now,
$\sqrt{12}=\sqrt{4\cdot 3}=2\sqrt{3}$
$\sqrt{20}=\sqrt{4\cdot 5}=2\sqrt{5}$
Thus,
$2(2\sqrt{5}-2\sqrt{3})$
Factor the two,
$4(\sqrt{5}-\sqrt{3})$

5. Oh right, I get it now..thanks a lot.