Year 5 Maths: Square Numbers and Square Roots

Understanding Square Numbers

What is a Square Number?

A square number is a number that you get when you multiply a whole number by itself. For example:

• If you take the number 3 and multiply it by itself (3 × 3), you get 9. So, 9 is a square number.
• Another example: 4 × 4 = 16, so 16 is also a square number.

List of Some Square Numbers

Here are the first few square numbers to help you remember:

• 1 (because 1 × 1 = 1)
• 4 (because 2 × 2 = 4)
• 9 (because 3 × 3 = 9)
• 16 (because 4 × 4 = 16)
• 25 (because 5 × 5 = 25)
• 36 (because 6 × 6 = 36)
• 49 (because 7 × 7 = 49)
• 64 (because 8 × 8 = 64)
• 81 (because 9 × 9 = 81)
• 100 (because 10 × 10 = 100)

Key Rules for Square Numbers

• Only whole numbers can be squared.
• The square of a number is always positive or zero.
• The square of a negative number is also positive (for example, (-3) × (-3) = 9).

Fun Tip

You can remember the square numbers by thinking of them as “building blocks.” Each number stacks on top of itself!

Understanding Square Roots

What is a Square Root?

A square root is the opposite of a square number. It is the number that, when multiplied by itself, gives you the original number.

For example:

• The square root of 9 is 3, because 3 × 3 = 9.
• The square root of 16 is 4, because 4 × 4 = 16.

How to Write Square Roots

We use the symbol

• The square root of 9 is written as $$\sqrt{9} = 3$$ .
• The square root of 16 is written as $$\sqrt{16} = 4$$ .

Key Rules for Square Roots

• The square root of a number is always a positive number or zero.
• If the number is a square number, it will have a whole number as a square root.
• If the number is not a square number, its square root will be a decimal or a fraction (for example, $$\sqrt{2}$$ is about 1.41).

Fun Tip

You can think of square roots as “finding the number that fits.” It’s like a puzzle where you’re looking for the piece that fits perfectly!

Questions

Easy Level Questions

1. What is the square of 5?
2. What is the square root of 16?
3. What is the square of 8?
4. What is the square root of 25?
5. What is $$3^2$$ ?
6. What is $$\sqrt{36}$$ ?
7. What is the square of 6?
8. What is the square root of 49?
9. What is $$4^2$$ ?
10. What is $$\sqrt{1}$$ ?
11. What is the square of 10?
12. What is the square root of 0?
13. What is $$2^2$$ ?
14. What is $$\sqrt{4}$$ ?
15. What is the square of 9?
16. What is the square root of 64?
17. What is $$5^2$$ ?
18. What is $$\sqrt{81}$$ ?
19. What is the square of 3?
20. What is the square root of 100?

Medium Level Questions

1. What is the square of 12?
2. What is the square root of 144?
3. Calculate $$7^2$$ .
4. Find $$\sqrt{121}$$ .
5. What is the square of 15?
6. What is the square root of 49?
7. What is $$10^2$$ ?
8. Find $$\sqrt{169}$$ .
9. What is the square of 11?
10. What is the square root of 81?
11. What is $$8^2$$ ?
12. Find $$\sqrt{225}$$ .
13. What is the square of 14?
14. What is the square root of 196?
15. Calculate $$9^2$$ .
16. What is the square root of 256?
17. What is $$6^2$$ ?
18. Find $$\sqrt{324}$$ .
19. What is the square of 13?
20. What is the square root of 400?

Hard Level Questions

1. What is the square of 17?
2. Find $$\sqrt{625}$$ .
3. What is $$14^2$$ ?
4. Find $$\sqrt{484}$$ .
5. What is the square of 19?
6. What is the square root of 529?
7. Calculate $$15^2$$ .
8. Find $$\sqrt{676}$$ .
9. What is the square of 18?
10. What is the square root of 729?
11. What is $$16^2$$ ?
12. Find $$\sqrt{841}$$ .
13. What is the square of 20?
14. What is the square root of 900?
15. Calculate $$17^2$$ .
16. What is $$\sqrt{961}$$ ?
17. What is the square of 21?
18. Find $$\sqrt{1024}$$ .
19. What is $$19^2$$ ?
20. What is the square root of 1210?

Answers and Explanations

Easy Level Answers

1. 25
2. 4
3. 64
4. 5
5. 9
6. 6
7. 36
8. 7
9. 16
10. 1
11. 100
12. 0
13. 4
14. 2
15. 9
16. 8
17. 25
18. 9
19. 9
20. 10

Medium Level Answers

1. 144
2. 12
3. 49
4. 11
5. 225
6. 7
7. 100
8. 13
9. 121
10. 9
11. 64
12. 15
13. 196
14. 14
15. 81
16. 16
17. 100
18. 18
19. 169
20. 20

Hard Level Answers

1. 289
2. 25
3. 196
4. 22
5. 361
6. 23
7. 225
8. 26
9. 324
10. 27
11. 256
12. 29
13. 400
14. 30
15. 289
16. 31
17. 441
18. 32
19. 361
20. 32

I hope this helps you understand square numbers and square roots better! Remember to practice, and soon it will all make sense!