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

  1. What is $$\sqrt[3]{216}$$?
  2. What is $$\sqrt[3]{343}$$?
  3. What is $$\sqrt[3]{729}$$?
  4. Estimate $$\sqrt[3]{50}$$.
  5. What number do you multiply by itself three times to get 125?
  6. What is the cube root of -64?
  7. If $$\sqrt[3]{x} = 4$$, what is x?
  8. If $$\sqrt[3]{y} = -3$$, what is y?
  9. What is $$\sqrt[3]{1000}$$?
  10. What is the cube root of 512?

Hard Level Questions

  1. What is the cube root of 1728?
  2. If $$\sqrt[3]{x} = 5$$, what is $$x$$?
  3. What is the cube root of -1000?
  4. Calculate $$\sqrt[3]{729} + \sqrt[3]{8}$$.
  5. If $$\sqrt[3]{z} = 2$$, what is $$z^3$$?
  6. Find the cube root of 1331.
  7. What is $$\sqrt[3]{-512}$$?
  8. What is the cube root of 3375?
  9. If $$\sqrt[3]{p} = 3$$, what is $$p^3$$?
  10. 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

  1. 6
  2. 7
  3. 9
  4. Between 3 and 4 (approximately 3.68)
  5. 5
  6. -4
  7. 64
  8. -27
  9. 10
  10. 8

Hard Level Answers

  1. 12
  2. 125
  3. -10
  4. 11
  5. 8
  6. 11
  7. -8
  8. 15
  9. 27
  10. Between 3 and 4 (approximately 3.11)

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