2.16: Rationalising to show a surd identity

0606/23/O/N/16 — Question 1 · 3 marks

(a)
Without using a calculator, show that 5+335+3=k2\dfrac{\sqrt{5} + 3\sqrt{3}}{\sqrt{5} + \sqrt{3}} = \sqrt{k} - 2 where kk is an integer to be found.
[3]