How do you multiply #2\sqrt { 2x ^ { 2} } \cdot 3\sqrt { 5x ^ { 2} }#?

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Answer 1 · 2017-06-26T00:46:36

See a solution process below:

First, rewrite the expression as:

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

Next, use this rule of exponents to multiply the radicals:

#sqrt(color(red)(a)) * sqrt(color(blue)(b)) = sqrt(color(red)(a) * color(blue)(b))#

#6(sqrt(color(red)(2x^2)) * sqrt(color(blue)(5x^2))) = 6sqrt(color(red)(2x^2) * color(blue)(5x^2)) = 6sqrt((2 * 5) * (x^2 * x^2)) =#

#6sqrt(10 * x^4) = 6sqrt(10) * sqrt(x^4) = 6sqrt(10) * x^2 =#

#6x^2sqrt(10)#