How do you simplify #(sqrt(20x^4)sqrt(5x))/(sqrt(4x^3))#?

1 Answer
Alan P.
Apr 9, 2015

#sqrt(20x^4) = (2x)(x)*sqrt(5)#
#sqrt(5x) = sqrt(5)*sqrt(x)#
#sqrt(4x^3) = (2x)*sqrt(x)#

So #(sqrt(20x^4)sqrt(5x))/sqrt(4x^3)#
can be written as
#((2x)(x)(sqrt(5))(sqrt(5))(sqrt(x)))/((2x)(sqrt(x))#

Simplifying:
#((cancel(2x))(x)(sqrt(5))(sqrt(5))(cancel(sqrt(x))))/(cancel((2x))(cancel(sqrt(x)))#
and combining the two #sqrt(5)# components:

#(sqrt(20x^4)sqrt(5x))/sqrt(4x^3) = 5x#

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