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Evaluate (sqrt(60) + 3*sqrt(7))^2 * (sqrt(60) - 3*sqrt(7))^2.

 Dec 1, 2019
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Simplify the following:
(sqrt(60) + 3 sqrt(7))^2 (sqrt(60) - 3 sqrt(7))^2

(sqrt(60) - 3 sqrt(7))^2 = 63 - 6 sqrt(105) - 6 sqrt(105) + 60 = 123 - 12 sqrt(105):


(sqrt(60) + 3 sqrt(7))^2 123 - 12 sqrt(105)

Factor 3 out of 123 - 12 sqrt(105) giving 3 (41 - 4 sqrt(105)):


(sqrt(60) + 3 sqrt(7))^2 3 (41 - 4 sqrt(105))

(sqrt(60) + 3 sqrt(7))^2 = 63 + 6 sqrt(105) + 6 sqrt(105) + 60 = 123 + 12 sqrt(105):


12 sqrt(105) + 123 3 (41 - 4 sqrt(105))

Factor 3 out of 123 + 12 sqrt(105) giving 3 (4 sqrt(105) + 41):


3 (4 sqrt(105) + 41) 3 (41 - 4 sqrt(105))

3×3 = 9:
9 (4 sqrt(105) + 41) (41 - 4 sqrt(105))

 

(4 sqrt(105) + 41) (41 - 4 sqrt(105)) = 41×41 + 41 (-4 sqrt(105)) + 4 sqrt(105)×41 + 4 sqrt(105) (-4 sqrt(105)) = 1681 - 164 sqrt(105) + 164 sqrt(105) - 1680 = 1:


  = 9

 Dec 1, 2019

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