11 Plus Practice Questions: Squares and Square Roots
26 October 2026
Understanding squares and square roots
Squares and square roots are key number properties in 11+ maths. A square number is a value made by multiplying a whole number by itself. The square root is the opposite: it finds the original number that was squared.
Why these skills matter for the 11+
Questions about squares and square roots often appear in 11+ exams. Children may be asked to identify square numbers, calculate a square root, or spot patterns involving these values. Mastering these skills helps with number fluency and problem solving.
Tips for practising squares and roots
Encourage your child to memorise square numbers up to at least 12 × 12. Practise spotting square numbers in lists and word problems. Use flashcards or quick quizzes to reinforce recall. For square roots, focus on recognising which numbers have whole number roots, and practise working backwards from a square number to its root.
Worked example
Find the square of 7.
7 × 7 = 49.
Now, find the square root of 49.
The square root of 49 is 7.
Key insight: Children who can move confidently between squares and square roots are better equipped to tackle a range of number problems in the 11+ exam.
How to practise independently
Children can use interactive worksheets, minigames and instant feedback tools to build confidence with squares and square roots. Revisiting mistakes and tracking progress helps target revision where it is needed most. Practising a little and often is usually more effective than cramming.
