Help with simplifying square roots

**d4rkh4z3** · September 3rd 2007, 04:47 PM

Well, my teacher explained to use how to simplify squares roots but i forgot how to do it, and now i have to finsh the homework. Can any1 explain to me how to do this? Here are some problems i have to do.
square root of 12, -square root-200, and 5 square root 50 - 3 square root 2 +4 square root 8
the - are negatives.

**Krizalid** · September 3rd 2007, 04:49 PM

$\sqrt{12}=\sqrt{2^2\times3}$

Can you take it from there?

**d4rkh4z3** · September 3rd 2007, 04:54 PM

she taught us how to Break it down to like 12 to square root 2 x square root 6
then square root 2 x square root 2 x square root 2. But i forgot how to finish it.

**topsquark** · September 3rd 2007, 08:56 PM

Originally Posted by Krizalid

$\sqrt{12}=\sqrt{2^2\times3}$

Can you take it from there?

Originally Posted by d4rkh4z3

she taught us how to Break it down to like 12 to square root 2 x square root 6
then square root 2 x square root 2 x square root 2. But i forgot how to finish it.

Do you mean $\sqrt{12} = \sqrt{2} \sqrt{2} \sqrt{3}$ ? How bizarre!

Well, note that you have two factors of $\sqrt{2}$ , so $\sqrt{2}\sqrt{2} = 2$ and we have:
$\sqrt{12} = \sqrt{2} \sqrt{2} \sqrt{3} = 2\sqrt{3}$ .

I find it easier (and faster) using Krizalid's method:
$\sqrt{12} = \sqrt{2^2 \cdot 3} = \sqrt{2^2} \sqrt{3} = 2 \sqrt{3}$
where I have included some steps that many would skip after some amount of experience.

-Dan

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