How do you multiply #4\sqrt { 15a } \cdot 4\sqrt { 3a }#?

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Answer 1 · 2018-03-11T22:07:31

See a solution process below:

First, rewrite the expression as:

#4 * 4 * sqrt(15a)sqrt(3a) =>#

#16sqrt(15a)sqrt(3a)#

Next, use this rule for radicals to combine the radicals:

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

#16sqrt(color(red)(15a)) * sqrt(color(blue)(3a)) =>#

#16sqrt(color(red)(15a) * color(blue)(3a)) =>#

#16sqrt(45a^2)#

Then, rewrite the term in the radical as:

#16sqrt(9a^2 * 5)#

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

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

#16sqrt(color(red)(9a^2) * color(blue)(5)) =>#

#16sqrt(color(red)(9a^2)) * sqrt(color(blue)(5)) =>#

#16 * 3a * sqrt(color(blue)(5)) =>#

#48asqrt(5)#