How do you simplify #(9+3sqrt6) /sqrt3#?

1 Answer
Shwetank Mauria
Feb 18, 2016

#3sqrt3+3sqrt2#

Explanation:

To simplify #(9+3sqrt6)/sqrt3#, we have to first rationalize denominator. Here as denominator is pure irrational number #sqrt3#, we multiply numerator and denominator both by #sqrt3#.

The fraction than becomes

#((9+3sqrt6)/sqrt3)*sqrt3/sqrt3# or

#(9sqrt3+3sqrt6*sqrt3)/(sqrt3*sqrt3)#, which simplifies to

#(9sqrt3+3sqrt18)/3# or #(9sqrt3+3*3sqrt2)/3# or

#3sqrt3+3sqrt2#

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