Example 1 · level 1 — a gentle start
What is 11 squared?
- 1331
- 22
- 121
- 122
Answer: 121 — Multiply 11 by itself twice.
11+ squares, cubes and roots questions
Squares, cubes and roots comes up in the maths paper of every major 11+ format. Here is what the questions look like, the method that works under time pressure, and five worked examples with the full reasoning, from a gentle start to a hard paper.
Maths · examined by GL and CEM · 5 worked examples
What your child needs to know
- Squared means times ITSELF, not times two. 5 squared is 25, not 10.
- Cubed means times itself three times: 3 cubed is 3 × 3 × 3 = 27.
Where marks get lost: A root asks the question backwards: the square root of 49 is the number that makes 49 when squared.
Worked examples
Every question below is generated by the same engine your child practises on, and every answer is derived by our checker rather than written by hand — which is why we can put them on a public page at all.
Example 2 · level 2 — typical of early practice
What is the square root of 64?
- 32
- 9
- 4
- 8
Answer: 8 — Which number times itself twice makes 64?
Example 3 · level 3 — standard paper difficulty
What is 15 squared?
- 226
- 3375
- 225
- 30
Answer: 225 — Multiply 15 by itself twice.
Example 4 · level 4 — a harder paper
What is the cube root of 2197?
- 14
- 47
- 732.3333333333334
- 13
Answer: 13 — Which number times itself three times makes 2197?
Example 5 · level 5 — the level that separates candidates
What is 11 cubed?
- 121
- 1342
- 1331
- 33
Answer: 1331 — Multiply 11 by itself three times.
How to practise this at home
- Work in short, frequent sessions. Ten minutes daily beats an hour at the weekend, because the recall gap is what builds memory.
- Insist on written working, even for questions your child can do in their head — under exam pressure the method is what survives.
- When an answer is wrong, ask them to explain their reasoning before you correct it. The error is almost always in one step, not the whole approach.
Practise squares, cubes and roots with a tutor that explains
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