2.2: Simplifying surds and solving a linear equation

0606/21/M/J/17 — Question 2 · 6 marks

Do not use a calculator in this question.

(a)
Show that 24×27+93015\sqrt{24} \times \sqrt{27} + \dfrac{9\sqrt{30}}{\sqrt{15}} can be written in the form a2a\sqrt{2}, where aa is an integer.
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(b)
Solve the equation 3(1+x)=2(x−3)\sqrt{3}(1 + x) = 2(x - 3), giving your answer in the form b+c3b + c\sqrt{3}, where bb and cc are integers.
[3]