CAIE IGCSE Mathematics Extended E1.18 Surds Question Bank

Practise simplifying surds, expanding brackets with square roots and rationalising denominators into exact simplified forms.

Syllabus
2028–2030
Topic
E1.18
Level
Extended

Exam points

  • simplify sums or differences of surds by extracting square factors before combining terms
  • expand brackets with surds and collect terms into forms
  • rationalise denominators using a single surd factor or a conjugate, then simplify

Covered syllabus points

E1.18.1 Understand and use surds, including simplifying expressions.E1.18.2 Rationalise the denominator

E1.18 Surds question 1

[Maximum number: 4]

Question (a)

(a)

(3−5)(2+35)=a+b5(3-\sqrt5)(2+3\sqrt5)=a+b\sqrt5
Find the value of a and the value of b.
a=b=\begin{aligned}a&=\\b&=\end{aligned}

a=b=\begin{aligned} & a= \\ & b= \end{aligned}

[ 2 ]

Question (b)

(b)

Rationalise the denominator.

Write your answer in its simplest form.

62\frac{6}{\sqrt{2}}

[ 2 ]
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