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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