SOLUTION: solve Sqrt {2+sqrt {3}}

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Question 1117168: solve Sqrt {2+sqrt {3}}
Found 2 solutions by Alan3354, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Not an equation.
Nothing to solve.

Answer by MathTherapy(10702) About Me  (Show Source):
You can put this solution on YOUR website!
solve Sqrt {2+sqrt {3}}

solve SIMPLIFY sqrt%282+%2B+sqrt%283%29%29

sqrt%282+%2B+sqrt%283%29%29 = sqrt%281%282+%2B+sqrt%283%29%29%29 = sqrt%28%282%282+%2B+sqrt%283%29%29%29%2F2%29 ----- Multiplying RADICAND, 2+%2B+sqrt%283%29 by 1 = 2%2F2
                        = sqrt%28%284+%2B+2sqrt%283%29%29%2F2%29
                        = sqrt%28%283+%2B+1+%2B+2sqrt%283%2A1%29%29%2F2%29 ----- Replacing 4 with 3 + 1, and 3 with 3*1
                        = sqrt%28%283+%2B+1+%2B+2sqrt%283%29%2Asqrt%281%29%29%2F2%29
                        =  ---- Converting 3 to %28sqrt%283%29%29%5E2, and 1 to %28sqrt%281%29%29%5E2
The numerator, %28sqrt%283%29%29%5E2+%2B+%28sqrt%281%29%29%5E2+%2B+2sqrt%283%29%2Asqrt%281%29 is in the form: %28a+%2B+b%29%5E2, with a being sqrt%283%29, and b being sqrt%281%29

                      So,  now becomes:
                          sqrt%28%28%28sqrt%283%29+%2B+sqrt%281%29%29%5E2%29%2F2%29 
                          sqrt%28%28sqrt%283%29+%2B+sqrt%281%29%29%5E2%29%2Fsqrt%282%29%29 --- Applying sqrt%28a%2Fb%29+=+sqrt%28a%29%2Fsqrt%28b%29
                          %28sqrt%283%29+%2B+sqrt%281%29%29%2Fsqrt%282%29 ----- Cancelling square and sqrt in NUMERATOR
                          %28%28sqrt%283%29+%2B+sqrt%281%29%29%2Fsqrt%282%29%29+%2A+%28sqrt%282%29%2Fsqrt%282%29%29 ------ Rationalizing DENOMINATOR
                          sqrt%282%29%28sqrt%283%29+%2B+sqrt%281%29%29%2F%28sqrt%282%29%2Asqrt%282%29%29%29 = highlight_green%28highlight%28%28sqrt%286%29+%2B+sqrt%282%29%29%2F2%29%29