2.15: Simplifying surd fractions

0606/23/M/J/20 — Question 5 · 6 marks

Do not use a calculator in this question.

(a)
Simplify 12872\dfrac{\sqrt{128}}{\sqrt{72}}.
[2]
(b)
Simplify 11+3−33+23\dfrac{1}{1 + \sqrt{3}} - \dfrac{\sqrt{3}}{3 + 2\sqrt{3}}, giving your answer as a fraction with an integer denominator.
[4]