CAIE IGCSE Mathematics E1.18.1 Understand & use surds, including simplifying expressions.

Practise simplifying surds, expanding brackets with surd terms and writing exact answers in forms such as a+b√n.

Exam points

simplify surd sums or differences by extracting square factors before collecting terms
expand brackets containing surds and collect the result into exact a+b√n form
use surd side lengths or area information to calculate an exact rectangle value

[Maximum number: 2]

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

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

$\begin{aligned}a&=-9\\b&=7\end{aligned}$

B1 for each
or for three correct terms from $6+9\sqrt5-2\sqrt5-3\sqrt5\sqrt5$ oe

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