# Simplify the expression `(6sqrt6)/(-4sqrt30)`  Give the exact value in simplified form. Rationalize any denominators.   6 times the square root of 6            over -4 times the square...

Simplify the expression `(6sqrt6)/(-4sqrt30)`  Give the exact value in simplified form. Rationalize any denominators.

6 times the square root of 6

over

-4 times the square root of 30

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To simplify:

`(6sqrt6)/(-4sqrt30)`

First simplify by cross cancelling and reduce the contents of the square roots to prime bases:

`therefore = (3sqrt(3 times 2))/(-2sqrt(5 times 2 times 3))`

Note we can now cross cancel further:

`therefore = 3/(-2sqrt5)`

To rationalize the denominator multiply by `sqrt5/sqrt5` which is effectively multiplying by `1/1 = 1`

`therefore = (3/(-2sqrt5)) times (sqrt5/sqrt5)`

`therefore = (3sqrt5)/(-2 sqrt5 times sqrt5)`

Note that `sqrt 5 times sqrt 5 = 5`

`therefore = (3sqrt5)/-10`     or `-(3sqrt5)/10`

Sources:

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

`=(-6/4)(sqrt(6)/sqrt(30))`

`=(-3/2)(sqrt(6)/(sqrt(5)sqrt(6)))`

`=(-3/2)(1/sqrt(5))`

`` Rationalise the denominators, you will get

`=(-3/2)((1xxsqrt(5))/(sqrt(5)sqrt(5)))`

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

`=(-3/(2xx5))sqrt(5)`

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