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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