How do you simplify 9/root3(36)?

1 Answer
Johnson Z.
Mar 15, 2016

(3root(3)(6))/2

Explanation:

1. Since the denominator of the fraction contains a cube root, we need to multiply the numerator and denominator by a value that will result in the denominator of 9/root(3)(36) to have a perfect cube. Thus, start by multiplying the numerator and denominator by root(3)(6).

9/root(3)(36)

=9/root(3)(36)(root(3)(6)/root(3)(6))

2. Simplify.

=(9root(3)(6))/root(3)(36*6)

=(9root(3)(6))/root(3)(216)

=(9root(3)(6))/6

=(color(red)cancelcolor(black)9^3root(3)(6))/color(red)cancelcolor(black)6^2

3. Rewrite the fraction.

=color(green)(|bar(ul(color(white)(a/a)(3root(3)(6))/2color(white)(a/a)|)))

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