I am trying to simplify the end of this half angle problem

How do I get from $\displaystyle \sqrt{(9-\sqrt{17})/(18)}$

to:

$\displaystyle (1/3)\sqrt{(9-\sqrt{17})/(2)}$

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- Mar 21st 2012, 11:40 AM #1

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- Mar 21st 2012, 11:58 AM #2

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## Re: Help

Working backwards:

Since the two is on the denominator it is essentially multiplying the (9-(17)^(1/2)) by 1/2. So to get 1/3 into the denominator you would square it, which becomes 1/9. then you would multiply it by everything else which will get the denominator to be 18.

Working Forwards:

$\displaystyle \sqrt{(9-\sqrt{17})/(18)}$ =

$\displaystyle \sqrt{(9-\sqrt{17})(1/18)}$ =

$\displaystyle \sqrt{(9-\sqrt{17})(1/2)(1/9)}$ =

$\displaystyle (1/3)\sqrt{(9-\sqrt{17})(1/2)}$ =

$\displaystyle (1/3)\sqrt{(9-\sqrt{17})/(2)}$

- Mar 25th 2012, 12:11 PM #3