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5. Rationalize the denominator of the following :
i)\(1/\sqrt{7}\)
ii)\(1/{\sqrt{7} - \sqrt{6}}\)
iii)\(1/{\sqrt{5} + \sqrt{2}}\)
iv)\(1/{\sqrt{7} - 2}\)
Answer :

To rationalize the denominator, we need to multiply the irrational denominator by it's conjugate.
i) = \(1/\sqrt{7}\) × \(\sqrt{7}/\sqrt{7}\)
= \(\sqrt{7}/7\)

ii) = \(1/(\sqrt{7} - \sqrt{6})\) × \((\sqrt{7} + \sqrt{6})/(\sqrt{7} + \sqrt{6})\)
= \((\sqrt{7} + \sqrt{6})/(7-6)\)
= \({\sqrt{7} + \sqrt{6}}\)

iii) = \(1/(\sqrt{5} + \sqrt{2})\) × \((\sqrt{5} - \sqrt{2})/(\sqrt{5} - \sqrt{2})\)
\( = (\sqrt{5} - \sqrt{2})/(5 - 2)\)
= \( (\sqrt{5} - \sqrt{2})/3\)

iv) = \(1/(\sqrt{7} - 2)\) × \((\sqrt{7} + 2)/(\sqrt{7} + 2)\)
=\( (\sqrt{7} + 2)/(7 - 4)\)
=\( {\sqrt{7} - 2}/3\)