How to solve the following question without a calculator?

Question

#(((√2)/2)*9)/((√3)/2)#

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Answer 1 · 2018-01-21T18:08:19

#3*sqrt6#

Multiply the numerator and denominator of the "big" fraction by #2# so you get rid of the denominators of the "small" fractions.

#(sqrt2*9)/sqrt3#

We know #9=3*3=sqrt3*sqrt3*sqrt3*sqrt3# so a pair of #sqrt3# terms cancels out from the fraction.

#sqrt2*sqrt3*sqrt3*sqrt3#

#=3*sqrt2*sqrt3#

#=3*sqrt(2*3)=3*sqrt6#

Because #sqrta*sqrtb=sqrt(ab)# if #a,b >=0#.