Squares and Square Roots Practice for 11+ Maths
26 October 2026
Understanding squares and square roots
Squares and square roots are important number skills for the 11+ maths exam. Children are expected to know the squares of numbers up to at least 12 and to find square roots for familiar values.
What is a square number
A square number is the result of multiplying a whole number by itself. For example, 6 × 6 = 36, so 36 is a square number.
What is a square root
The square root is the number that, when multiplied by itself, gives the original number. For example, the square root of 49 is 7, because 7 × 7 = 49.
Worked example
Find the square root of 81.
First, ask: what number times itself equals 81?
Try 9 × 9 = 81.
So the square root of 81 is 9.
Key insight: Spotting square numbers
Learning the most common square numbers (1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144) helps your child quickly answer questions and recognise patterns in 11+ maths.
Practice questions to try at home
1. What is the square of 8?
2. What is the square root of 64?
3. Which of these is a square number: 18, 25, 30?
4. Find the square root of 100.
Supporting your child
Encourage your child to practise both finding squares and square roots. Use quick recall games or flashcards to help them remember the key facts.
