# Find Cubes and Cube Roots

In this worksheet, students will find the answers to cube powers and cube roots to enable them to work these out without a calculator.

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel, OCR, Eduqas, AQA

Curriculum topic:   Number, Indices and Surds

Curriculum subtopic:   Structure and Calculation, Powers and Roots

Difficulty level:

### QUESTION 1 of 10

We have looked before at finding a square number and a square root.

In this activity, we're going to explore cube numbers and cube roots.

Cube numbers are reached when you multiply a number by itself twice.

e.g. 63 = 6 x 6 x 6 = 216

A cube root is the opposite of a cube number.

To find one, you need to ask yourself the question:

"I have to multiply three numbers that are the same to reach this number. What must the numbers be?"

e.g. Find the cube root of 27.

27 = __ x __ x __

The only number that could fit here (since they all have to be the same) is 3.

27 = 3 x 3 x 3

So the cube root of 27 is 3.

In this activity, we will find the answers to cube powers and cube roots so that we are able to work these out without a calculator.

Match each cubed number to its value.

## Column B

23
8
43
64
63
125
53
216

Match each cube root to its answer.

## Column B

∛216
1
∛1
4
∛8
2
∛64
6

State if the cube numbers below have been calculated correctly.

State if the cube roots below have been calculated correctly.

What is the cube of 5?

What is the cube root of 0.064?

Cubing a number always make it bigger.

When is this statement true?

Always

Sometimes

Never

Which is larger?

32 or 23

23

32

Complete the sentence below to define a cube number

23

32

Complete the sentence below to define how to find a cube number

23

32

• Question 1

Match each cubed number to its value.

## Column B

23
8
43
64
63
216
53
125
EDDIE SAYS
Just remember that when you are finding the cube of a number, you have to multiply that number by itself a total of three times. 23 = 2 x 2 x 2 = 8 43 = 4 x 4 x 4 = 64 63 = 6 x 6 x 6 = 216 53 = 5 x 5 x 5 = 125 How many matches did you find here?
• Question 2

Match each cube root to its answer.

## Column B

∛216
6
∛1
1
∛8
2
∛64
4
EDDIE SAYS
When we want to find cube roots, we need to look at what number we have to multiply by itself, and then again, to find our target value. 1 x 1 x 1 = 1 so ∛1 = 1 2 x 2 x 2 = 8 so ∛8 = 2 4 x 4 x 4 = 64 so ∛64 = 4 6 x 6 x 6 = 216 so ∛216 = 6 You may need to use trial and error to find your answer but, similarly to square numbers, it can be really helpful to commit the most common cube numbers to memory to help you spot these quickly.
• Question 3

State if the cube numbers below have been calculated correctly.

EDDIE SAYS
The most common mistake with cubes (and powers in general) is that using the power number as a multiplier rather than using it to tell you how many times to multiply a number by itself. So 23 = 2 x 2 x 2 (8) not 2 x 3 (6) 1 x 1 x 1 = 1 so 3 is not the correct answer 2 x 2 x 2 = 8 so this calculation is correct 4 x 4 x 4 = 64 so 12 is not the correct answer 1 x 1 x 1 = 1 so this calculation is now correct
• Question 4

State if the cube roots below have been calculated correctly.

EDDIE SAYS
The easiest mistake to make here is to confuse cube roots with square roots. When working with square roots, we are looking for two numbers to multiply. With cube roots, it's three numbers to find. Ask yourself: "Which number can I multiply by itself twice to reach 8 or 9 or 27 or 216?" As you become more familiar with cube numbers, these will become easier to spot. Don't worry if you found this tricky; let's practise some more.
• Question 5

What is the cube of 5?

125
EDDIE SAYS
Worded questions can be a little bit confusing. What does "cube of" mean here? It's just means: 53? So we need to do 5 x 5 x 5 = 125
• Question 6

What is the cube root of 0.064?

0.4
EDDIE SAYS
The only cube number we can link these decimals to is 43. Therefore, we know our answer must include the number 4 somewhere. So as 4 x 4 x 4 = 64 Then ∛0.064 = 0.4 Does that make sense?
• Question 7

Cubing a number always make it bigger.

When is this statement true?

Sometimes
EDDIE SAYS
This statement is usually true, but only if number being cubed is greater than 1. 1 x 1 x 1 = 1 so this is an example which disproves this statement. 2 x 2 x 2 = 8 which is bigger, so this statement must be 'sometimes' true. This is a useful rule to mention so that you can quickly check if your answer looks correct or not.
• Question 8

Which is larger?

32 or 23

32
EDDIE SAYS
All we have to do here is to work these calculations out: 32 = 3 x 3 = 9 23 = 2 x 2 x 2 = 8 Which number out of 9 and 8 is larger? Hopefully you did not get your squares and cubes mixed up there!
• Question 9

Complete the sentence below to define a cube number

EDDIE SAYS
To find a cube number, we multiply three of the same numbers together. The answer to this calculation is called a cube number. e.g. 2 x 2 x 2 = 8 So the cube number here is 8. Pretty simple, right?
• Question 10

Complete the sentence below to define how to find a cube number

EDDIE SAYS
The key fact here is that we need to use three numbers, which are all identical, in a multiplication sum to make a cube number. Hopefully you are feeling more confident to apply this fact now! You may want to revise square numbers now, so that you can compare these two types to each other.
---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

### What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started