How do you simplify #(3sqrt7 - 6sqrt5)(4sqrt7 + 8sqrt5)#?

1 Answer
May 18, 2018

Answer:

#(3sqrt7-6sqrt5)(4sqrt7+8sqrt5)=-156#

Explanation:

Simplifying would mean getting rid of as many square roots as possible. We should, therefore, multiply it out.

First we note that 3 is common in the first parenthesis, and 4 is common in the second. Therefore:

#(3sqrt7-6sqrt5)(4sqrt7+8sqrt5)#
#=3(sqrt7-2sqrt5)*4(sqrt7+2sqrt5)#

You should know that #(a-b)(a+b)=a^2-b^2#,
which means that #(sqrt7-2sqrt5)(sqrt7+2sqrt5)=7-2^2*5=-13#

Therefore #=3(sqrt7-2sqrt5)*4(sqrt7+2sqrt5)=-3*4*13=-156#

Ergo #(3sqrt7-6sqrt5)(4sqrt7+8sqrt5)=-156#