How do you multiply #-3\sqrt { 6p ^ { 2} } \cdot 4\sqrt { 12p }#?

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Answer 1 · 2017-07-19T02:16:04

See a solution process below:

First, rewrite the expression as:

#(-3 * 4)(sqrt(6p^2)sqrt(12p)) =>#

#-12sqrt(6p^2)sqrt(12p)#

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

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

#-12sqrt(6p^2)sqrt(12p) => -12sqrt(6p^2 * 12p) =>#

#-12sqrt(72p^3)#

We can now rewrite the term in the radical as:

#-12sqrt(36p^2 * 2p)#

We can use this rule (the reverse of the above rule) to simplify the expression:

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

#-12sqrt(36p^2 * 2p) => -12sqrt(36p^2)sqrt(2p) =>#

#(-12 * 6p)sqrt(2p) =>#

#-72psqrt(2p)#