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

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Answer 1 · 2015-04-17T11:43:22

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

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

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