By rationalising the denominator of \(\frac{1}{5+\sqrt{7}}\), we get __________(a) \(\frac{5-\sqrt{7}}{5+\sqrt{7}}\)(b) \(\frac{5-\sqrt{7}}{18}\)(c) \(\frac{5+\sqrt{7}}{18}\)(d) \(\frac{5+\sqrt{7}}{5-\sqrt{7}}\)This question was posed to me in an online quiz.My question is based upon Representing Real Numbers on the Number Line & Real Numbers Operations in section Number Systems of Mathematics – Class 9

By rationalising the denominator of \(\frac{1}{5+\sqrt{7}}\), we get _

1.	By rationalising the denominator of \(\frac{1}{5+\sqrt{7}}\), we get __________(a) \(\frac{5-\sqrt{7}}{5+\sqrt{7}}\)(b) \(\frac{5-\sqrt{7}}{18}\)(c) \(\frac{5+\sqrt{7}}{18}\)(d) \(\frac{5+\sqrt{7}}{5-\sqrt{7}}\)This question was posed to me in an online quiz.My question is based upon Representing Real Numbers on the Number Line & Real Numbers Operations in section Number Systems of Mathematics – Class 9
Answer» Right choice is (b) \(\frac{5-\sqrt{7}}{18}\) Explanation: When the denominator of an expression contains a term with a SQUARE root, the process of CONVERTING it to an equivalent expression whose denominator is a rational number is called rationalising the denominator. By MULTIPLYING \(\frac{1}{5+\sqrt{7}}\) by \(5-\sqrt{7}\), we will GET same expression since \(\frac{5-\sqrt{7}}{5-\sqrt{7}}\) = 1. Therefore, \(\frac{1}{5+\sqrt{7}} = {\frac{1}{5+\sqrt{7}}} * (\frac{5-\sqrt{7}}{5-\sqrt{7}})\) = \(\frac{5-\sqrt{7}}{(55)-(\sqrt{7}\sqrt{7})}\) = \(\frac{5-\sqrt{7}}{25-7}\) = \(\frac{5-\sqrt{7}}{18}\).

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