Edexcel IGCSE Math A 1.1.F brackets and hierarchy of operations

Practise order-of-operations questions by evaluating powers first and placing brackets so a calculation gives the stated result.

Exam points

Evaluate calculations with powers, multiplication or division before addition and subtraction.
Place brackets in a calculation so the given equality becomes true after evaluation.

[Maximum number: 4]

Express $\frac{3+\sqrt{8}}{(\sqrt{2}-1)^{2}}$ in the form $p+\sqrt{q}$ where p and q are integers.
Show each stage of your working clearly.

$(\sqrt2-1)^2=3-2\sqrt2$

Rationalising factor:
$(3+2\sqrt2)$

Final answer:
$17+\sqrt{288}$

Equivalent statement: p=17, q=288, from fully correct working.

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1.1.F Brackets and the hierarchy of operations question 1