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

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Answer 1 · 2015-09-03T23:27:35

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

(assuming $x >= 0$ )

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:

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

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

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