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# Cubes and cube roots
- URL: https://www.esheets.io/cubes-and-cube-roots/
- Published: 2025-11-11T16:54:01.000Z
- Updated: 2026-06-21T18:16:53.000Z
- Author: Richard Linnington
- Tags: Maths, Number

Cubic numbers and cube roots often appear when working with volume – like figuring out how much water a cube-shaped tank can hold, or how big a box needs to be to store a certain number of smaller cubes. Understanding cubes and their roots helps you think in three dimensions and solve problems involving space, design, and engineering. [Jump to the questions](#practise-now)

## Practise now

Worksheet preview and key skills 

### Worksheet preview

Practise cubes and cube roots with this self-marking maths worksheet.

The interactive worksheet below generates questions, gives instant feedback, and lets students record their score.

#### What you’ll practise

- Recognising cube numbers.
- Cubing a number by multiplying it by itself three times.
- Finding cube roots of cube numbers.
- Understanding that cubing and cube rooting are inverse operations.

Use the interactive worksheet below, or read the [Topic guide](#topic-guide) for the method and worked example.

Solve the following cubes and cube roots. 

## Topic guide

### What this worksheet practises

This worksheet provides practice on calculating cubes and cube roots. A cube number is the result of multiplying a number by itself, and then by itself again. The cube root is the exact opposite operation. These calculations are essential for finding the volume of 3D shapes.

### Key method

Cubing a number and finding a cube root are inverse (opposite) operations.

- To cube a number (written as x³), calculate: x × x × x.
- To find a cube root (written as ³√x), you are looking for the number which, when multiplied by itself three times, gives 'x'.
- Memorising the first five cube numbers is highly recommended to save time in non-calculator exams.

### Worked example

**Calculate 4³ and then find the cube root of 125.**

Step 1: Calculate 4³.

4³ means 4 × 4 × 4.

4 × 4 = 16.

16 × 4 = 64.

So, 4³ = 64.

Step 2: Find ³√125.

We need a number that, multiplied by itself three times, equals 125\. Since it ends in a 5, the root is very likely 5.

5 × 5 × 5 = 25 × 5 = 125.

So, ³√125 = 5.

### Common mistakes to avoid

The most frequent error is multiplying the base number by 3 instead of cubing it. For example, incorrectly thinking that 4³ = 4 × 3 = 12\. You must multiply the number by itself. Another mistake is confusing square roots with cube roots when looking at the radical symbol; always look for the small '3' outside the root.

### Things to remember

The first five cube numbers are: 1, 8, 27, 64, and 125\. Knowing these off by heart will make exam questions significantly easier and faster to solve.