How do you simplify #4sqrt (81 / 8)#?
See a solution process below:
First, using this rule of radicals rewrite the expression:
Next, rewrite the denominator and use this rule of exponents to simplify the denominator:
To rationalize the denominator or eliminate the radical from the denominator we can multiply by the appropriate form of
#sqrt(a/b) = sqrt(a)/sqrt(b)#
When simplifying square roots of fractions such as this example, I like to make the denominator into a perfect square first.
So we find:
#4sqrt(81/8) = 4sqrt((81*2)/16) = 4sqrt((9^2*2)/4^2) = 4*9/4sqrt(2) = 9sqrt(2)#