Edexcel IGCSE Math B 1.E rationalising denominators

Practise rationalising questions by multiplying by the conjugate, simplifying surd products and matching the requested exact surd form.

Exam points

Multiply numerator and denominator by the conjugate to remove a surd denominator.
Simplify surd products and collect terms into forms such as a plus b root 2.
Show non-calculator working when proving a fraction has the requested exact form.

[Maximum number: 3]

Answer parts (a) and (b).

Express $\frac{12}{\sqrt5-1}$ in the form $y\sqrt x+y$ , where x and y are integers.
Show each stage of your working.

$\frac{12}{\sqrt5-1}\times\frac{\sqrt5+1}{\sqrt5+1} =\frac{12(\sqrt5+1)}{5-1}$ $=\frac{12\sqrt5+12}{4} =3\sqrt5+3$

Final answer:
$3\sqrt5+3$

M1 for multiplying by the conjugate. M1 for correct denominator/numerator simplification. A1; allow $3+3\sqrt5$ , but not $3(\sqrt5+1)$ .

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1.E Rationalising denominators question 1