2.13: Rationalising and expanding surd squares

0606/23/M/J/16 — Question 5 · 6 marks

Do not use a calculator in this question.

(a)
Express 87−5\dfrac{\sqrt{8}}{\sqrt{7} - \sqrt{5}} in the form a+b\sqrt{a} + \sqrt{b}, where aa and bb are integers.
[3]
(b)
Given that 28+p3=(q+23)228 + p\sqrt{3} = (q + 2\sqrt{3})^{2}, where pp and qq are integers, find the values of pp and of qq.
[3]