How to simplify #root(3)(24y^21x^5)# ?

1 Answer
EZ as pi
Apr 2, 2017

#2xy^7root(3)(2x^2)#

Explanation:

Write the radicand as aproduct of prime factors.

#root(3) (24y^21x^5) =root(3) (3xx2^3y^21x^5)#

Write cubes where possible:
#root(3) (3xx2^3y^21x^5) = root(3) (3xxcolor(red)(2^3y^21x^3)xx x^2)#

Find the cube roots where possible by dividing the indices by #3#.

#=color(red)(2xy^7)root(3)(2x^2)#

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