How do you rationalize the denominator and simplify root3(9/7)?

1 Answer
Johnson Z.
Mar 15, 2016

root(3)(441)/7

Explanation:

1. Since the denominator contains a cube root, we need to multiply the numerator and denominator by a value that will result in the denominator of root(3)(9/7) to have a perfect cube. Thus, start by multiplying the numerator and denominator by root(3)(49).

root(3)(9/7)

=root(3)(9)/root(3)(7)

=root(3)(9)/root(3)(7)(root(3)(49)/root(3)(49))

2. Simplify.

=root(3)(441)/root(3)(343)

=color(green)(|bar(ul(color(white)(a/a)root(3)(441)/7color(white)(a/a)|)))

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