How do you simplify (9sqrt2)/sqrt(6)?

1 Answer
Ricardo A.
Jul 1, 2016

3sqrt(3)

Explanation:

First we recognize that 6=2*3
That allows us to write sqrt(6) as sqrt(2*3)
Square roots of multiplications can be split so sqrt(2*3)=sqrt(2)*sqrt(3)
So,(9sqrt(2))/(sqrt(2)*sqrt(3))
That will allow us to eliminate the sqrt(2) from the top and bottom leaving us with 9/sqrt(3)
Now we split 9 into 3*3 and further split one of those 3s into sqrt(3)*sqrt(3)
leaving: (3*sqrt(3)*sqrt(3))/sqrt(3)
Eliminate one of the sqrt(3) from the top and the one from the bottom leaving us with the final answer of:
3sqrt(3)

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