Year 6 Maths: Cube Roots

What is a Cube Root?

Hello, Year 6! Today, we are going to learn about cube roots. A cube root is a number that, when multiplied by itself three times, gives you a certain number. Let’s break it down:

• If you have a number, let’s say 27, the cube root of 27 is the number that you can multiply by itself three times to get 27.
• In this case, the cube root of 27 is 3 because: $$3 \times 3 \times 3 = 27$$

How Do We Write Cube Roots?

We use a special symbol to show cube roots. The cube root of a number (x) is written as:

$$\sqrt[3]{x}$$

So, for our example:

$$\sqrt[3]{27} = 3$$

Key Rules to Remember

1. Multiplication: When you multiply a number by itself three times, you find the cube.
   • For example, (2 \times 2 \times 2 = 8). So, $$\sqrt[3]{8} = 2$$ .
2. Negative Numbers: The cube root of a negative number is also negative.
   • For example, $$\sqrt[3]{-27} = -3$$ because:
   $$-3 \times -3 \times -3 = -27$$ .
3. Perfect Cubes: Some numbers are called perfect cubes because their cube roots are whole numbers.
   • Examples: (1), (8), (27), (64), and (125).

Tips and Tricks

• Memorise Small Perfect Cubes: Here are some small perfect cubes to remember:
  • (1^3 = 1)
  • (2^3 = 8)
  • (3^3 = 27)
  • (4^3 = 64)
  • (5^3 = 125)
• Use Estimation: If you’re unsure, try to estimate where the cube root might fall. For instance, if you want to find the cube root of 50, you know:
  • $$\sqrt[3]{27} = 3$$ and $$\sqrt[3]{64} = 4$$ .
  • So, $$\sqrt[3]{50}$$ is somewhere between 3 and 4.

Practice Questions

Easy Level Questions

1. What is $$\sqrt[3]{1}$$ ?
2. What is $$\sqrt[3]{8}$$ ?
3. What is $$\sqrt[3]{27}$$ ?
4. What is $$\sqrt[3]{64}$$ ?
5. What is $$\sqrt[3]{125}$$ ?
6. What is $$\sqrt[3]{-1}$$ ?
7. What is $$\sqrt[3]{-8}$$ ?
8. What is $$\sqrt[3]{-27}$$ ?
9. What is $$\sqrt[3]{0}$$ ?
10. What is the cube root of 1,000,000?

Medium Level Questions

11. What is $$\sqrt[3]{216}$$ ?
12. What is $$\sqrt[3]{343}$$ ?
13. What is $$\sqrt[3]{729}$$ ?
14. Estimate $$\sqrt[3]{50}$$ .
15. What number do you multiply by itself three times to get 125?
16. What is the cube root of -64?
17. If $$\sqrt[3]{x} = 4$$ , what is x?
18. If $$\sqrt[3]{y} = -3$$ , what is y?
19. What is $$\sqrt[3]{1000}$$ ?
20. What is the cube root of 512?

Hard Level Questions

21. What is the cube root of 1728?
22. If $$\sqrt[3]{x} = 5$$ , what is $$x$$ ?
23. What is the cube root of -1000?
24. Calculate $$\sqrt[3]{729} + \sqrt[3]{8}$$ .
25. If $$\sqrt[3]{z} = 2$$ , what is $$z^3$$ ?
26. Find the cube root of 1331.
27. What is $$\sqrt[3]{-512}$$ ?
28. What is the cube root of 3375?
29. If $$\sqrt[3]{p} = 3$$ , what is $$p^3$$ ?
30. Estimate $$\sqrt[3]{30}$$ .

Answers to Questions

Easy Level Answers

1. 1
2. 2
3. 3
4. 4
5. 5
6. -1
7. -2
8. -3
9. 0
10. 100

Medium Level Answers

11. 6
12. 7
13. 9
14. Between 3 and 4 (approximately 3.68)
15. 5
16. -4
17. 64
18. -27
19. 10
20. 8

Hard Level Answers

21. 12
22. 125
23. -10
24. 11
25. 8
26. 11
27. -8
28. 15
29. 27
30. Between 3 and 4 (approximately 3.11)

Happy learning, everyone! Keep practising cube roots, and soon you’ll be a pro!