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

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Answer 1 · 2018-05-18T18:06:58

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

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

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