Someone help me solve this easy Math task?

Mathematics
Tutor: None Selected Time limit: 1 Day

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Please deduct it and write how you got the answer. Thank you in advance!

Oct 1st, 2015

Hello!

(5√20 + √45 - 7√5 - 4√28 + 3√7)*(2√80 - 2√5 + 2√63 + √28 - 3√7) =

[here we extract perfect squares from the square roots, for example √20 = √(4*5) = √4*√5 = 2√5 ]

(10√5 + 3√5 - 7√5 - 8√7 + 3√7)*(8√5 - 2√5 + 6√7 + 2√7 - 3√7) =

[here we group √5's and √7's together]

(6√5 - 5√7)*(6√5 + 5√7) =

[here we use (a+b)*(a-b) = a^2 - b^2 ]

(6√5)^2 - (5√7)^2 =

5*36 - 5*35 =

5*1 = 5.

Please ask if something is unclear.
Oct 1st, 2015

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