SOLUTION: I'm working on half-angle identities for trigonometry and I keep getting the wrong answer, or possibly in a different form than the book's answer. I'll just ask about the answer

Algebra ->  Radicals -> SOLUTION: I'm working on half-angle identities for trigonometry and I keep getting the wrong answer, or possibly in a different form than the book's answer. I'll just ask about the answer      Log On


   

Question 1206442: I'm working on half-angle identities for trigonometry and I keep getting the wrong answer, or possibly in a different form than the book's answer.
I'll just ask about the answer which is basically rationalizing a root problem (with a fractional root within it).
I keep getting stuck on an intermediary step, as follows, from the solution in the book:
sqrt(1+sqrt(5))/sqrt2
which gives the solution:
sqrt(50-10sqrt(5))/10
I know I'm messing up with rationalizing the denominator and I can't figure it out.
I ran the plain text radicals above in Wolfram Alpha and it comes out basically as the problem/solution in the book.
Any help would be greatly appreciated.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


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The student has corrected the given expression. See further down for how the given answer is the correct equivalent form of the given expression.

Note also that the sign in the solution is "+", not "-".

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The answer you show is not equivalent to the given expression; perhaps in your book you are looking at the answer to a different problem.

sqrt%281%2Bsqrt%285%29%29%2Fsqrt%282%29 = 1.272 to 3 decimal places

sqrt%2850-10sqrt%285%29%29%2F10 = 0.526 to 3 decimal places

To rationalize the denominator in the given expression, we only need to multiply numerator and denominator by sqrt(2):



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Corrected original expression: sqrt%281%2B%28sqrt%285%29%2F5%29%29%2Fsqrt%282%29

Multiply numerator and denominator by sqrt(2):

sqrt%282%29%28sqrt%281%2B%28sqrt%285%29%2F5%29%29%29%2F2=sqrt%282%2B2sqrt%285%29%2F5%29%2F2

Combine fractions inside the radical:

%28sqrt%28%2810%2B2sqrt%285%29%29%2F5%29%29%2F2

Multiply numerator and denominator in the radical by 5 to rationalize the denominator in the radical; and simplify: