Question

How do you simplify `4 sqrt (81 / 8)`?

Answer 1

You can play around with the fraction that's under the square root and get

`E = 4sqrt(81/8) = 4 * (sqrt(81))/(sqrt(8)) = 4 * 9/(sqrt(4 * 2)) = 4 * 9/(sqrt(4) * sqrt(2))`

`E = stackrel(color(blue)(2))(cancel(4)) * 9/(cancel(2) * sqrt(2)) = 18/sqrt(2)`

Rationalize the denominator to get

`E = (18 * sqrt(2))/(sqrt(2) * sqrt(2)) = (18 * sqrt(2))/(2) = (stackrel(color(blue)(9))(cancel(18)) * sqrt(2))/(cancel(2)) = color(green)(9sqrt(2))`