How do you simplify #sqrt(18a^2)*4sqrt(3a^2)#?

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Answer 1 · 2018-06-02T12:38:03

See a solution process below:

First, use this rule for radicals to rewrite the expression:

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

#sqrt(color(red)(18a^2)) * 4sqrt(color(blue)(3a^2)) =>#

#4sqrt(color(red)(18a^2)) * sqrt(color(blue)(3a^2)) =>#

#4sqrt(color(red)(18a^2) * color(blue)(3a^2)) =>#

#4sqrt(54a^4)#

Next, rewrite the expression as:

#4sqrt(color(red)(9a^4) * color(blue)(6))#

Now, use this rule for radicals to complete the simplification:

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

#4 * sqrt(color(red)(9a^4)) * sqrt(color(blue)(6)) =>#

#4 * 3a^2 * sqrt(6) =>#

#12a^2sqrt(6)#