Question

How do you simplify `(6sqrt 18) / (4 sqrt 8)`?

Answer 1

`(6sqrt 18) / (4 sqrt 8) = color(green)( 9 / 4 = 2.25`

Explanation:

`(6sqrt 18) / (4 sqrt 8) = (3*cancel(2)*sqrt(3^2*2))/(2*cancel(2)*sqrt(2^2*2))`

We know that `color(blue)(sqrt(a*b) = sqrta*sqrtb`

`= (3*sqrt(3^2)*cancel(sqrt2))/(2*sqrt(2^2)*cancel(sqrt2))`

`= (3*3)/(2*2)`

`=color(green)( 9 / 4 = 2.25`