How do you simplify #-4sqrt8*sqrt10#?

1 Answer
Jul 3, 2017

Answer:

See a solution process below:

Explanation:

First, use this rule for radicals to rewrite the expression:

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

#-4sqrt(color(red)(8)) * sqrt(color(blue)(10)) = -4sqrt(color(red)(8) * color(blue)(10)) = -4sqrt(80)#

Next, rewrite the expression and use the same rule for radicals:

#-4sqrt(80) = -4sqrt(color(red)(16) * color(blue)(5)) = -4sqrt(color(red)(16)) * sqrt(color(blue)(5)) = (-4 * 4)sqrt(5) =#

#-16sqrt(5)#