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

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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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