Help understanding simplification of problem with radicals and exponents

**Jkoziol** · April 18th 2012, 08:49 PM

Hello,
Im working on trying to learn trigonometry but my lack of a comprehensive understanding of algebra and basic math is holding me back here.

I am working on a problem using an online tutoring website and after asking the computer for help solving the problem it gave me an answer but I don't understand how it got there.

The original problem looks like this: (((3^.5)/3)^2+1)^.5

and it was simplified to this: (2(3^.5))/3

How was this done can someone explain the steps so I get a better understanding of the basic arithmetic going on here I would rather know how its done than continue to rely on the calculator like I have done for far too long with some obvious negative results. Thanks for any help you guys can give!

**Prove It** · April 18th 2012, 08:59 PM

Originally Posted by Jkoziol

Hello,
Im working on trying to learn trigonometry but my lack of a comprehensive understanding of algebra and basic math is holding me back here.

I am working on a problem using an online tutoring website and after asking the computer for help solving the problem it gave me an answer but I don't understand how it got there.

The original problem looks like this: (((3^.5)/3)^2+1)^.5

and it was simplified to this: (2(3^.5))/3

How was this done can someone explain the steps so I get a better understanding of the basic arithmetic going on here I would rather know how its done than continue to rely on the calculator like I have done for far too long with some obvious negative results. Thanks for any help you guys can give!

$\displaystyle \begin{align*} \sqrt{\left(\frac{\sqrt{3}}{3}\right)^2 + 1} &= \sqrt{\frac{\left(\sqrt{3}\right)^2}{3^2} + 1} \\ &= \sqrt{\frac{3}{9} + 1} \\ &= \sqrt{\frac{1}{3} + 1} \\ &= \sqrt{\frac{1}{3} + \frac{3}{3}} \\ &= \sqrt{\frac{4}{3}} \\ &= \frac{\sqrt{4}}{\sqrt{3}} \\ &= \frac{2}{\sqrt{3}} \\ &= \frac{2}{ \sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} \\ &= \frac{2\sqrt{3}}{3} \end{align*}$

**Jkoziol** · April 24th 2012, 04:10 PM

Thanks for the help I have one more problem for you.

Here is another simplification I don't understand

1/cosx=(2*3^.5)/3 and it was simplified to cosx=(3^.5)/2

If anyone could help me out it would be greatly appreciated.

**skeeter** · April 24th 2012, 04:36 PM

Originally Posted by Jkoziol

Thanks for the help I have one more problem for you.

Here is another simplification I don't understand

1/cosx=(2*3^.5)/3 and it was simplified to cosx=(3^.5)/2

If anyone could help me out it would be greatly appreciated.

$\frac{1}{\cos{x}} = \frac{2\sqrt{3}}{3}$

$\frac{\cos{x}}{1} = \frac{3}{2\sqrt{3}}$

now ... what is 3 divided by its own square root?

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