2.6: Expanding and rationalising surd expressions

0606/21/O/N/18 — Question 3 · 7 marks

Do not use a calculator in this question.

(a)
Simplify (2+25)(42−35)(\sqrt{2} + 2\sqrt{5})(4\sqrt{2} - 3\sqrt{5}), giving your answer in the form a+bca + b\sqrt{c}, where aa, bb and cc are integers.
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(b)
Simplify 4−363+2\dfrac{4 - 3\sqrt{6}}{\sqrt{3} + \sqrt{2}}, giving your answer in the form p3+q2p\sqrt{3} + q\sqrt{2}, where pp and qq are integers.
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