Question

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$\frac{1}{(3 - \sqrt{8)} } - \ \frac{1}{( \sqrt{8 - \sqrt{7} } )} + \frac{1}{( \sqrt{7 - \sqrt{6} )} } - \frac{1}{( \sqrt{6 - \sqrt{5} )} } + \frac{1}{ (\sqrt{7 - 6} )} = 5$
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Answer 1

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Answer 2

$\frac{1}{(3 - \sqrt{8)} } - \ \frac{1}{( \sqrt{8 - \sqrt{7} } )} + \frac{1}{( \sqrt{7 - \sqrt{6} )} } - \frac{1}{( \sqrt{6 - \sqrt{5} )} } + \frac{1}{ (\sqrt{7 - 6} )} = 5$

After Rationalization of denominator of LHS, we get

$\frac{3+√8}{9-8} - \frac{√8+√7}{8-7} + \frac{√7+√6}{7-6} - \frac{√6+√5}{6-5} + \frac{√5+2}{5-4} = 5$

$3 + \cancel{√8} - \cancel{√8} - \cancel{√7} + \cancel{√7} + \cancel{√6} - \cancel{√6} - \cancel{√5} + \cancel{√5} + 2 = 5$

$3+2= 5$