---
title: "Integer powers and roots"
description: "Use integer powers and associated real roots (square, cube, and higher); recognise powers of 2, 3, 4, and 5; distinguish between exact representations of roots and their decimal approximations"
canonical: https://lightmysky.com/learn/mathematics/integer-powers-and-roots-mt_hCVPYlF-7Y
source: https://lightmysky.com/learn/mathematics/integer-powers-and-roots-mt_hCVPYlF-7Y.md
retrieved: 2026-09-02
---

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# Integer powers and roots

Use integer powers and associated real roots (square, cube, and higher); recognise powers of 2, 3, 4, and 5; distinguish between exact representations of roots and their decimal approximations

Subject: Mathematics · Area: Number Representation & Place Value · Ages 11 to 14
Page: https://lightmysky.com/learn/mathematics/integer-powers-and-roots-mt_hCVPYlF-7Y

## Ready when they can

- Calculate squares, cubes, and higher integer powers of whole numbers
- Find square roots and cube roots of perfect squares and perfect cubes
- Recognise key powers (powers of 2 up to 2¹⁰, powers of 3 up to 3⁵, etc.) and distinguish exact roots from approximations

## Lesson: Integer powers and roots

A square number comes from multiplying a whole number by itself. We write this as n², which means n × n. For example, 4² = 4 × 4 = 16.

*(drawing: This grid has 3 rows and 3 columns, so it holds 3² = 9 dots in total.)*

A cube number comes from multiplying a whole number by itself three times. We write this as n³, which means n × n × n. For example, 10³ = 10 × 10 × 10 = 1000.

**Example.** Priya wants to find 5² and 3³. She works out 5² = 5 × 5 = 25, and 3³ = 3 × 3 × 3 = 27. Squaring and cubing start the same way, but cubing multiplies by the number one more time.

The small raised number is the power. It counts how many copies of the number you multiply, so 2⁴ = 2 × 2 × 2 × 2 = 16. Learn the key ones: the powers of 2 double each time, 2, 4, 8, 16, 32, 64, and the powers of 3 are 3, 9, 27, 81, 243.

Going backwards from a power is called finding a root. The square root symbol √ asks: what number times itself gives this? √25 = 5, because 5² = 25. The cube root symbol ∛ asks: what number multiplied by itself three times gives this? ∛27 = 3, because 3³ = 27.

Not every root is exact. √25 = 5 exactly, because 5² = 25. But √50 falls between 7 and 8, because 7² = 49 and 8² = 64, so we say it is close to 7 rather than exact.

**Recap.** Squaring multiplies a number by itself once, cubing multiplies it twice more, and the root symbols √ and ∛ undo them, though not every root comes out as a whole number.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Order of operations with powers and roots](https://lightmysky.com/learn/mathematics/order-of-operations-with-powers-and-roots-mt_X5cypSGoGU)

## Opens up

- [Number Sets & Infinity](https://lightmysky.com/learn/mathematics/number-sets-and-infinity-mt_b4lbTOJYwI)
- [Powers of Ten Notation](https://lightmysky.com/learn/mathematics/powers-of-ten-notation-mt_bO-njVOige)
- [Laws of Exponents](https://lightmysky.com/learn/mathematics/laws-of-exponents-mt_UjNba32kkz)
- [Pythagoras' Theorem](https://lightmysky.com/learn/mathematics/pythagoras-theorem-mt_1VmTUxBrNd)