Rationalise the denominators of the following:

$fraction numerator 1 over denominator square root of 7 minus 2 end fraction equals fraction numerator 1 over denominator square root of 7 minus 2 end fraction cross times fraction numerator square root of 7 plus 2 over denominator square root of 7 plus 2 end fraction$

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Solution

fraction numerator 1 over denominator square root of 7 minus 2 end fraction fraction numerator 1 over denominator square root of 7 minus 2 end fraction equals fraction numerator 1 over denominator square root of 7 minus 2 end fraction cross times fraction numerator square root of 7 plus 2 over denominator square root of 7 plus 2 end fraction

Multiplying and dividing by

square root of 7 plus 2

equals fraction numerator square root of 7 plus 2 over denominator 7 minus 4 end fraction equals fraction numerator square root of 7 plus 2 over denominator 3 end fraction.

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