1.3: Rationalising, surd simplification and quadratic equation

0606/11/M/J/18 — Question 10 · 9 marks

Do not use a calculator in this question.

(a)

Simplify

\dfrac{5 + 6\sqrt{5}}{6 + \sqrt{5}}

[3]

(b)

Show that

3^{0.5} \times (\sqrt{2})^{7}

can be written in the form

a\sqrt{b}

, where

a

and

b

are integers and

a > b

[2]

(c)

Solve the equation

x + \sqrt{2} = \dfrac{4}{x}

, giving your answers in simplest surd form.

[4]