What is a square number?

A square number is what you get when you multiply a whole number by itself, such as 4 × 4 = 16. The dots can be arranged into a perfect square with equal rows and columns, which is where the name comes from.

What does "squared" mean?

"Squared" means a number multiplied by itself. For example, 6 squared means 6 × 6 = 36. It is written with a small raised 2, like 6².

Why is it written with a small 2, like 5²?

The small raised 2 (an exponent) tells you to use the number as a factor twice. So 5² means 5 × 5, not 5 × 2. It is a short way of writing "five squared".

What are the first square numbers?

The first square numbers are 1, 4, 9, 16, 25, 36 and 49 — that is 1², 2², 3², 4², 5², 6² and 7². Notice the gaps between them get larger each time.

How can my child tell if a number is a perfect square?

Try arranging that many dots into a square with equal rows and columns — if it works exactly with none left over, it is a perfect square. For example, 16 makes a neat 4-by-4 square, but 12 cannot form a square, so it is not a square number.

Square Numbers and What Squared Means

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A square number is the result of multiplying a whole number by itself — for example, 3 × 3 = 9, so 9 is a square number. The name comes from geometry: that many dots (or tiles) can be arranged into a perfect square with the same number of rows as columns. The first few square numbers are 1, 4, 9, 16, 25 and 36, and they spread further apart as the numbers grow.

The word "squared" simply means a number multiplied by itself, written with a small raised 2 — so 5 squared is 5² = 5 × 5 = 25. Reading and writing this notation correctly is the key idea: the little 2 is not "times 2", it tells you to use the base number twice as a factor.

Square numbers matter because they appear all through later maths — finding the area of a square, working with square roots, recognising patterns, and eventually algebra and Pythagoras' theorem. Learners come away able to picture why a number is "square", to compute small squares by heart, and to spot which numbers are perfect squares and which are not.

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A square shape

🟪 Square Numbers A square number is what you get when dots can line up in a perfect square — the same number of rows as columns. 3 rows × 3 columns = 9 dots. So 9 is a square number! Tap Next to start building squares yourself. 👉
Build a square

Build the square 🧱 Tap the empty boxes to fill them in. Try to fill the whole grid and count how many dots make a square. Dots filled: 0 / 16 A 4 by 4 square is made of 16 dots. 4 rows of 4! ✨
What 'squared' means

What does “squared” mean? 🤔 “Squared” just means a number times itself. 5 × 5 = 25 We say: 5 squared is 25 And we write it with a tiny floating 2: 5² = 25 The little ² means “use this number two times in a multiply.” It does not mean 5 × 2! Tap each card to reveal the answer 👇 🔢2²?2×2 🔢3²?3×3 🔢6²?6×6
Slide to grow

Slide to grow a square 🌱 Move the slider to choose how many dots are on each side. Watch the square grow and see its square number. 1 × 1 = 1 Side length: 1 • drag me!
The square number list

The square number family 👨‍👩‍👧‍👦 Here are the first square numbers. Notice they get further and further apart! 1 4 9 16 25 36 49 1² 2² 3² 4² 5² 6² 7² 🔍 A cool pattern: the gaps go 3, 5, 7, 9… (odd numbers!) 1 +3→ 4 +5→ 9 +7→ 16 +9→ 25
Spot the square

Spot the square number 🕵️ One of these numbers is a perfect square (it makes a neat square of dots). Which one? Tap to try — you can try again! Which number is a square number? 12 16 20
Your turn

What is 4 squared? 💪 Remember: 4 squared means 4 × 4. Picture a 4-by-4 square of dots. Tap your answer. 8 16 12
You did it!

🎉 You’re a square-number star! What you learned: 🟪 A square number makes a perfect square of dots — same rows as columns. ✖️ “Squared” means a number times itself: 5 squared = 5 × 5 = 25. ✏️ We write it with a little ²: that means use the number two times. 👨‍👩‍👧 The family starts 1, 4, 9, 16, 25, 36, 49… and the gaps grow by odd numbers. Next time you see a tiny ², you’ll know exactly what to do. Well done! 🌟

Frequently asked questions

What is a square number?: A square number is what you get when you multiply a whole number by itself, such as 4 × 4 = 16. The dots can be arranged into a perfect square with equal rows and columns, which is where the name comes from.
What does "squared" mean?: "Squared" means a number multiplied by itself. For example, 6 squared means 6 × 6 = 36. It is written with a small raised 2, like 6².
Why is it written with a small 2, like 5²?: The small raised 2 (an exponent) tells you to use the number as a factor twice. So 5² means 5 × 5, not 5 × 2. It is a short way of writing "five squared".
What are the first square numbers?: The first square numbers are 1, 4, 9, 16, 25, 36 and 49 — that is 1², 2², 3², 4², 5², 6² and 7². Notice the gaps between them get larger each time.
How can my child tell if a number is a perfect square?: Try arranging that many dots into a square with equal rows and columns — if it works exactly with none left over, it is a perfect square. For example, 16 makes a neat 4-by-4 square, but 12 cannot form a square, so it is not a square number.

Square Numbers and What Squared Means

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Frequently asked questions

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