How do you simplify 9sqrt2(4sqrt6)9√2(4√6)?

1 Answer
smendyka
May 24, 2017

See a solution process below:

Explanation:

First, rewrite the expression as:

(9 * 4)(sqrt(2) * sqrt(6)) => 36(sqrt(2) * sqrt(6))(9⋅4)(√2⋅√6)⇒36(√2⋅√6)

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

sqrt(a) * sqrt(b) = sqrt(a * b)√a⋅√b=√a⋅b and sqrt(a * b) = sqrt(a) * sqrt(b)√a⋅b=√a⋅√b

36(sqrt(2) * sqrt(6)) => 36sqrt(2 * 6) => 36sqrt(12) =>36(√2⋅√6)⇒36√2⋅6⇒36√12⇒

36sqrt(4 * 3) => 36(sqrt(4) * sqrt(3)) => 36(2 * sqrt(3)) =>36√4⋅3⇒36(√4⋅√3)⇒36(2⋅√3)⇒

(36 * 2)sqrt(3) =>(36⋅2)√3⇒

72sqrt(3)72√3

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