1. ## Simplifying radicals in my trigonometry.

I am having a problem coming up with the correct solutions to work. The reason being I don't really understand how to work with radicals.

A simple example of my problem is this.

sqrt(33) * sqrt(32)

I know the answer is 4sqrt(66) but I have no idea why.

Another example of an answer I got in my problem that I cannot simplify is here &#40;-4&#47;-sqrt&#40;33&#41; &#43; -sqrt&#40;32&#41;&#47;2&#41; &#47;&#40; 1 &#43; -4&#47;sqrt&#40;33&#41; &#43; -sqrt&#40;32&#41;&#47;2 &#41; - Wolfram|Alpha. (sorry for the link wolfram's makes it look pretty)

I think I may have messed up some of the positives and negatives.
I am using the sum formula for tangent.
Tana = -4/-sqrt(33)
Tanb = -sqrt(32)/2

Can anybody point me in the direction of a radical tutorial somewhere or give me some pointers?

Thanks!

2. Originally Posted by Jkeeb
I am having a problem coming up with the correct solutions to work. The reason being I don't really understand how to work with radicals.

A simple example of my problem is this.

sqrt(33) * sqrt(32)

I know the answer is 4sqrt(66) but I have no idea why.

Another example of an answer I got in my problem that I cannot simplify is here &#40;-4&#47;-sqrt&#40;33&#41; &#43; -sqrt&#40;32&#41;&#47;2&#41; &#47;&#40; 1 &#43; -4&#47;sqrt&#40;33&#41; &#43; -sqrt&#40;32&#41;&#47;2 &#41; - Wolfram|Alpha. (sorry for the link wolfram's makes it look pretty)

I think I may have messed up some of the positives and negatives.
I am using the sum formula for tangent.
Tana = -4/-sqrt(33)
Tanb = -sqrt(32)/2

Can anybody point me in the direction of a radical tutorial somewhere or give me some pointers?

Thanks!
Well
$\displaystyle \sqrt{33} \cdot \sqrt{32} = \sqrt{33 \cdot 32} = \sqrt{3 \cdot 11 \cdot 2 \cdot 16} = \sqrt{16} \cdot \sqrt{6 \cdot 11}$

$\displaystyle = 4 \sqrt{66}$

As for your tangent formula, there is a mistake.
$\displaystyle tan(a + b) = \frac{tan(a) + tan(b)}{1 - tan(a) \cdot tan(b)}$

You subtracted the two tangents in Wolfram.

-Dan