How do you simplify #(2sqrt10)(4sqrt15)#?

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Answer 1 · 2017-05-25T00:57:43

See a solution process below:

First, rewrite the expression as:

#(2 * 4)(sqrt(10) * sqrt(15)) => 8(sqrt(10) * sqrt(15))#

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

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

#8(sqrt(10) * sqrt(15)) => 8sqrt(10 * 15) => 8sqrt(150)#

We can rewrite this as:

#8sqrt(25 * 6)#

We can use the above rule for radicals in reverse to simplify the radical term:

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

#8(sqrt(25 * 6)) = 8(sqrt(25) * sqrt(6)) => 8(5 * sqrt(6)) =>#

#(8 * 5)sqrt(6) =>#

#40sqrt(6)#