SOLUTION: [(sqrt(3+sqrt5)) - (sqrt(3-sqrt5))]^2 = 2

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Question 1117380: [(sqrt(3+sqrt5)) - (sqrt(3-sqrt5))]^2 = 2
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
[(sqrt(3+sqrt5)) - (sqrt(3-sqrt5))]^2 = 2
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Take the sqrt of both sides to get:
sqrt(3+sqrt(5)) - sqrt(3-sqrt(5)) = sqrt(2)
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2.2882 - 0.874 = 1.414
1.414 = 1.414
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Cheers,
Stan H.
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Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




Expand the binomial in the LHS



Collect like terms and calculate the product of conjugates in the center term of the LHS





John

My calculator said it, I believe it, that settles it