How do you simplify #9sqrt2(4sqrt6)#?

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Answer 1 · 2017-05-24T13:16:26

See a solution process below:

First, rewrite the expression as:

#(9 * 4)(sqrt(2) * sqrt(6)) => 36(sqrt(2) * sqrt(6))#

Next, use this rule for multiplying radicals and it's reverse to complete the simplification:

#sqrt(a) * sqrt(b) = sqrt(a * b)# and #sqrt(a * b) = sqrt(a) * sqrt(b)#

#36(sqrt(2) * sqrt(6)) => 36sqrt(2 * 6) => 36sqrt(12) =>#

#36sqrt(4 * 3) => 36(sqrt(4) * sqrt(3)) => 36(2 * sqrt(3)) =>#

#(36 * 2)sqrt(3) =>#

#72sqrt(3)#