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Simplify the expression. Give the exact value in simplified form.  Rationalize any...

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schooledmom | (Level 1) Salutatorian

Posted August 21, 2013 at 2:46 AM via web

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Simplify the expression. Give the exact value in simplified form.  Rationalize any demoninators.

6 times the square root of 6

over

-4 times the square root of 30

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aruv | High School Teacher | (Level 2) Valedictorian

Posted August 21, 2013 at 3:06 AM (Answer #1)

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`(6xxsqrt(6))/(-4xxsqrt(30))`

`sqrt(yx)=sqrt(y)xxsqrt(x)`

`sqrt(30)=sqrt(5xx6)=sqrt(5)xxsqrt(6)`

Thus

`(6xxsqrt(6))/(-4xxsqrt(30))=(6xxsqrt(6))/(-4xxsqrt(5)xxsqrt(6))`

`=6/(-4sqrt(5))`

`=(3xxsqrt(5))/(-2xxsqrt(5)xxsqrt(5))`

`=(3xxsqrt(5))/(-10)`

`=(-3xxsqrt(5))/10`

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