How do you evaluate #\root 3 ( 729x) \root 3 (8x^3 ) \sqrt { 125} #?

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Answer 1 · 2017-11-23T00:00:06

See a solution process below:

We can rewrite this expression as:

#root(3)(9^3 * x)root(3)(2^3x^3)sqrt(25 * 5) =>#

#root(3)(9^3 * x)root(3)(2^3x^3)sqrt(5^2 * 5)#

We can then use this rule for radicals to simplify the radicals:

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

#root(3)(color(red)(9^3) * color(blue)(x))root(3)(2^3x^3)sqrt(color(red)(5^2) * color(blue)(5)) =>#

#root(3)(color(red)(9^3))root(3)(color(blue)(x))root(3)(2^3x^3)sqrt(color(red)(5^2))sqrt(color(blue)(5)) =>#

#(9root(3)(x))(2x)(5sqrt(5)) =>#

#(9 * 2 * 5)root(3)(x)sqrt(5) =>#

#90root(3)(x)sqrt(5)#