How to solve the following question without a calculator?

(((√2)/2)*9)/((√3)/2)

1 Answer
Jan 21, 2018

3*sqrt6

Explanation:

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.