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Polynomials

Question

Wired Faculty App

Rationalise the denominators of the following:

$fraction numerator 3 plus square root of 7 over denominator 3 minus 4 square root of 7 end fraction$

Solution

fraction numerator 3 plus square root of 7 over denominator 3 minus 4 square root of 7 end fraction fraction numerator 3 plus square root of 7 over denominator 3 minus 4 square root of 7 end fraction equals fraction numerator 3 plus square root of 7 over denominator 3 minus 4 square root of 7 end fraction cross times fraction numerator 3 plus square root of 7 over denominator 3 plus 4 square root of 7 end fraction

Multliplying the numerator and denominator by

3 plus 4 square root of 7

equals fraction numerator left parenthesis 3 plus square root of 7 right parenthesis left parenthesis 3 plus 4 square root of 7 right parenthesis over denominator left parenthesis 3 right parenthesis squared minus left parenthesis 4 square root of 7 right parenthesis squared end fraction equals fraction numerator 3 left parenthesis 3 plus 4 square root of 7 right parenthesis plus square root of 7 left parenthesis 3 plus 4 square root of 7 right parenthesis over denominator 9 minus 112 end fraction equals space fraction numerator 9 plus 12 square root of 7 plus 3 square root of 7 plus 28 over denominator negative 103 end fraction equals fraction numerator 37 plus 15 square root of 7 over denominator negative 103 end fraction equals negative fraction numerator 37 plus 15 square root of 7 over denominator 103 end fraction

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