Calculate the value of

MATHEMATICS · Multi-part · ICSE · Mathematics · Pure Arithmetic · Pure Arithmetic

Problem

Calculate the value of S=77−5+77+5S = \displaystyle \frac{7}{\sqrt{7}-\sqrt{5}} + \frac{7}{\sqrt{7}+\sqrt{5}}, and express your answer in the simplest form. (i) Rationalize the denominator of each fraction separately. (ii) Add the two simplified fractions to obtain SS. (iii) State whether SS is a rational or an irrational number, giving a brief reason.

Related theory

Browse the problem library