How do you simplify #root3(7/3)#?

Question

1264 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-10-11T10:02:03

See a solution process below:

First, we can use this rule of radicals to rewrite expression:

#root(n)(color(red)(a)/color(blue)(b)) = root(n)(color(red)(a))/root(n)(color(blue)(b))#

#root(3)(color(red)(7)/color(blue)(3)) = root(3)(color(red)(7))/root(3)(color(blue)(3))#

To rationalize the denominator we can multiply the expression by the appropriate form of #1#:

#root(3)(9)/root(3)(9) xx root(3)(7)/root(3)(3) =>#

#(root(3)(9) xx root(3)(7))/(root(3)(9) xx root(3)(3)) =>#

#root(3)(9 xx 7)/(root(3)(9 xx 3)) =>#

#root(3)(63)/(root(3)(27)) =>#

#root(3)(63)/(root(3)(3^3)) =>#

#root(3)(63)/3#