Powers and Roots
Squares and cubes, the roots that undo them, powers of ten, and what that little raised number is actually counting.
No account, and the maths stays in your browser — more— less
This activity is for learning and practice. Anything it suggests is indicative only — it is not a formal assessment and not a substitute for a teacher or tutor.
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3⁴ is not 3 × 4
The small raised number does not join in the multiplication — it counts it. 3⁴ means four 3s multiplied together: 3 × 3 × 3 × 3, which is 81, not 12. This is the single most persistent mistake in the topic, and it survives into secondary school because the notation usually gets taught as a shorthand to remember rather than as an instruction to read.
That is why half the questions here run the other way: given 2 × 2 × 2 × 2, what is the index? Answer that comfortably and the 3 × 4 reading has nowhere left to live.
A root is the question asked backwards
“What is 7²?” and “what is √49?” are the same fact from opposite ends. Squaring asks what you get; rooting asks what you started with. There is no new arithmetic to learn — if you know your square numbers, you already know your square roots.
Why every root here comes out whole
√50 is 7.071… and needs a calculator and a conversation about rounding. That is a genuinely different lesson, so every number in this tool has an exact whole-number root. Nothing here is approximate.
School levels
School levels are a guide only. They show where a skill is usually taught in each country and are not taken from, aligned to, or endorsed by any curriculum authority. Your school may cover it earlier or later.