How do you simplify $(2x sqrt( 2x))(3 sqrt(5x))$ ?

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Answer 1 · 2016-04-30T12:22:51

If $x >= 0$ then

$(2xsqrt(2x))(3sqrt(5x))=6sqrt(10)x^2$

I will assume that we are dealing with $x>=0$ and Real square roots.

If $a, b >= 0$ then $sqrt(ab) = sqrt(a)sqrt(b)$

$(2xsqrt(2x))(3sqrt(5x))$

$= 2x*3*sqrt(2x*5x)$

$= 6xsqrt(10x^2)$

$= 6xsqrt(10)sqrt(x^2)$

$= 6xsqrt(10)x$

$=6sqrt(10)x^2$

How do you simplify (2x sqrt( 2x))(3 sqrt(5x))(2x sqrt( 2x))(3 sqrt(5x))?