Numeracy · Guided Practice

Surds

12 questions with answers and video solutions. Try each one before revealing the answer.

1
Simplify 12\displaystyle \sqrt{12}

No hints on this one — its full written solution is with the answer.

2
Simplify 372\displaystyle 3\sqrt{72}

No hints on this one — its full written solution is with the answer.

3
Simplify 220+645\displaystyle 2\sqrt{20} + 6\sqrt{45}

No hints on this one — its full written solution is with the answer.

4
Simplify 8×12\displaystyle \sqrt{8} \times \sqrt{12}

No hints on this one — its full written solution is with the answer.

5
Rationalise the denominator and simplify
4208\displaystyle \large\frac{4\sqrt{20}}{\sqrt8}\normalsize

No hints on this one — its full written solution is with the answer.

6
2014 P1 Q8
3 Marks
Express 40+410+90\displaystyle \sqrt{40}+4\sqrt{10}+\sqrt{90}
as a surd in its simplest form.
7
2018 P1 Q11
2 Marks

Express 96\displaystyle \frac{9}{\sqrt{6}} with a rational denominator.
Give your answer in its simplest form.

8
2019 P1 Q12
3 Marks

Express 240\displaystyle \frac{\sqrt{2}}{\sqrt{40}} as a fraction with a rational denominator.
Give your answer in its simplest form.

9
2022 P1 Q13
3 Marks

Expand and simplify 10(10−2)+85\displaystyle \sqrt{10}(\sqrt{10}-\sqrt{2})+8\sqrt{5}.

10
2023 P1 Q8
2 Marks
Express 1215\displaystyle \large\frac{12}{\sqrt{15}} with a rational denominator.
Give your answer in its simplest form.
11
2024 P1 Q6
2 Marks
Simplify 75−3.\displaystyle \sqrt{75}-\sqrt{3}.
12
2025 P1 Q12
2 Marks

Express 610\displaystyle \frac{6}{\sqrt{10}} with a rational denominator.
Give your answer in its simplest form.

Keep practising

More surds questions

New questions, modelled on past paper questions and checked against their marking instructions. Not reprints — you have not seen these before.

Practice questions courtesy of Maths.scot. Full written solutions are on his site — the links above go straight to them.

All practice topics