Square and Cube Number Exercises (Year 6) | CGP Plus - Free Printable

Let's solve the problem step by step.

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Task 1: True or False Statements

We need to determine whether each statement about square and cube numbers is true or false, and correct any false ones.

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1. You can square any number by multiplying it by 2.
✘ False
✔ Correction: You square a number by multiplying it by itself, not by 2.
For example: $ 3^2 = 3 \times 3 = 9 $, not $ 3 \times 2 = 6 $.
So, squaring means multiplying a number by itself.

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2. You can cube a number by multiplying it by itself twice.
✔ True
Cubing a number means multiplying it by itself three times (i.e., twice more), so:
$ 3^3 = 3 \times 3 \times 3 $ — this is multiplying by itself twice after the first 3.
So yes, "multiplying it by itself twice" gives the cube.

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3. The correct notation for a square number is number².
✔ True
Yes, the exponent 2 indicates squaring. For example, $ 5^2 = 25 $.

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4. The correct notation for a cube number is number⁴.
✘ False
✔ Correction: The correct notation for a cube number is number³, not number⁴.
For example, $ 3^3 = 27 $, not $ 3^4 = 81 $.
So, cubing uses exponent 3.

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✔ Summary of Task 1:

| Statement | True / False | Correction |
|---------|--------------|------------|
| 1. You can square any number by multiplying it by 2. | False | Square = multiply by itself, not by 2 |
| 2. You can cube a number by multiplying it by itself twice. | True | Correct |
| 3. The correct notation for a square number is number². | True | Correct |
| 4. The correct notation for a cube number is number⁴. | False | Should be number³ |

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Task 2: Complete the Table

We are given calculations and need to:
- Write the correct notation (e.g., $ 5^2 $),
- Say if it's a square or cube,
- Give the answer.

Let’s go row by row.

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#### Row 1: 2 × 2
Already done:
- Notation: $ 2^2 $
- Square
- Answer: 4

✔ Correct.

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#### Row 2: 5 × 5
- Correct Notation: $ 5^2 $
- Square or Cube: Square
- Answer: $ 5 \times 5 = 25 $

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#### Row 3: 4 × 4 × 4
- Correct Notation: $ 4^3 $
- Square or Cube: Cube
- Answer: $ 4 \times 4 \times 4 = 64 $

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#### Row 4: 3 × 3 × 3
- Correct Notation: $ 3^3 $
- Square or Cube: Cube
- Answer: $ 3 \times 3 \times 3 = 27 $

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#### Row 5: 8 × 8
- Correct Notation: $ 8^2 $
- Square or Cube: Square
- Answer: $ 8 \times 8 = 64 $

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#### Row 6: 1 × 1 × 1
- Correct Notation: $ 1^3 $
- Square or Cube: Cube
- Answer: $ 1 \times 1 \times 1 = 1 $

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✔ Final Completed Table:

| Calculation | Correct Notation | Square or Cube | Answer |
|------------|------------------|----------------|--------|
| 2 × 2 | $ 2^2 $ | Square | 4 |
| 5 × 5 | $ 5^2 $ | Square | 25 |
| 4 × 4 × 4 | $ 4^3 $ | Cube | 64 |
| 3 × 3 × 3 | $ 3^3 $ | Cube | 27 |
| 8 × 8 | $ 8^2 $ | Square | 64 |
| 1 × 1 × 1 | $ 1^3 $ | Cube | 1 |

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✔ Final Answers:

#### Task 1:
1. False – Squaring means multiplying by itself, not by 2.
2. True
3. True
4. False – Should be number³, not number⁴.

#### Task 2:
Completed table as above.

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