SOLUTION: If x = square root 5 + square root 8, find x + 1 over x giving answers in surd form with rational denominators

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Question 859005: If x = square root 5 + square root 8, find x + 1 over x giving answers in surd form with rational denominators
Answer by Awesom3guy(31) About Me  (Show Source):
You can put this solution on YOUR website!
x+=+sqrt+%285%29+%2B+sqrt+%288%29

%28x%2B1%29%2Fx=?

Plug in sqrt%285%29%2Bsqrt%288%29 in the places of x.

+%28+sqrt%285%29%2Bsqrt%288%29%2B1+%29+%2F+%28+sqrt%285%29%2Bsqrt%288%29+%29+

Now you want to rationalize the denominator by expanding the fraction with the DIFFERENCE of the roots in the denominator. When you multiply both the top and bottom with sqrt%285%29-sqrt%288%29, the roots in the denominator will be gone.
Because +%28+sqrt%28a%29+%2B+sqrt%28b%29+%29+%2A+%28+sqrt%28a%29+-+sqrt%28b%29+%29+=+a+-+b.

So:


=

When you expand the brackets on the top:

+%28+5+-+sqrt%2840%29+%2B+sqrt%2840%29+-+8+%2B+sqrt%285%29+-+sqrt%288%29+%29+%2F+%28-3%29

The -sqrt%2840%29+%2B+sqrt%2840%29 cancels out and you get:

+%28+-3+%2B+sqrt%285%29+-+sqrt%288%29+%29+%2F+%28-3%29

:) Hope I helped