Simplify the following expression completely by rationalising each denominator

MATHEMATICS · Multi-part · CBSE · Mathematics · Number Systems · Number Systems

Problem

Simplify the following expression completely by rationalising each denominator. Write every step clearly. (i) Rationalise the denominator of 5−27+22\displaystyle\frac{5-\sqrt{2}}{7+2\sqrt{2}} and write the fraction in its simplest form. (ii) State the rational value that appears in the denominator after rationalisation. (iii) Using your answer from part (i), calculate an approximate decimal value of the simplified expression correct to two decimal places.

Related theory

Browse the problem library