ICSE

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

Problem

Let

P=\dfrac{\sqrt{3}}{7-2\sqrt{3}}

and

Q=\dfrac{3\sqrt{3}}{7+2\sqrt{3}}

. (i) Rationalise the denominator of

P

and simplify your result. (ii) Rationalise the denominator of

Q

and simplify your result. (iii) Hence, or otherwise, find the exact value of

P+Q