How do you multiply radical expressions?

1 Answer
Jim H
Mar 22, 2015

One method is to make one big radical, then simplify.

#root(3)(2x^2y^6)root(3)(20xy^4)=root(3)(2x^2y^6*20x^2y^4)#

#=root(3)(40x^3y^10)=root(3)(8*5x^3y^9y)=2xy^3root(3)(5y)#

Or simplify first, then combine what's left and simplify again:

#root(3)(2x^2y^6)root(3)(20xy^4)=[y^2root(3)(2x^2)][yroot(3)(20xy)]#

#=y^3root(3)(40x^3y)=2xy^3root(3)(5y)#.

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