How do you simplify #sqrt(3x^3) * sqrt(6x^2)#?

1 Answer
George C.
Sep 3, 2015

#sqrt(3x^3)*sqrt(6x^2) = sqrt(18x^5)=3xsqrt(2x)#

(assuming #x >= 0#)

Explanation:

If #sqrt(a)# and #sqrt(b)# are Real, then #a, b >= 0# and #sqrt(a)sqrt(b) = sqrt(ab)#

In our case, if both #sqrt#'s are Real, then:

#sqrt(3x^3)*sqrt(6x^2) = sqrt(3x^3*6x^2) = sqrt(18x^5) = sqrt((3x^2)^2*2x)#

#= sqrt((3x^2)^2)sqrt(2x) = 3x^2sqrt(2x)#

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