Square Numbers and Perfect Squares
A square number is what you get when you multiply a whole number by itself: 4 × 4 = 16. It is called "square" because that many dots can be arranged into a perfect square, 4 rows of 4.
What is a square number?
Lay out 16 counters in 4 rows of 4 and you get a square. Try it with 15 or 17 counters and it will not work, which is why 16 is a square number and 15 is not.
We write 4² and say "four squared". Square numbers are also called perfect squares: both names mean a whole number times itself. In grade 3 children should know the first ten square numbers by heart: 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100.
List of perfect squares from 1 to 400
These are the squares of the numbers 1 to 20. Every perfect square up to 400 is on this list.
- 1² = 1 × 1 = 1
- 2² = 2 × 2 = 4
- 3² = 3 × 3 = 9
- 4² = 4 × 4 = 16
- 5² = 5 × 5 = 25
- 6² = 6 × 6 = 36
- 7² = 7 × 7 = 49
- 8² = 8 × 8 = 64
- 9² = 9 × 9 = 81
- 10² = 10 × 10 = 100
- 11² = 11 × 11 = 121
- 12² = 12 × 12 = 144
- 13² = 13 × 13 = 169
- 14² = 14 × 14 = 196
- 15² = 15 × 15 = 225
- 16² = 16 × 16 = 256
- 17² = 17 × 17 = 289
- 18² = 18 × 18 = 324
- 19² = 19 × 19 = 361
- 20² = 20 × 20 = 400
Patterns that help
- The gaps between square numbers are the odd numbers: 1, 4 (+3), 9 (+5), 16 (+7), 25 (+9) …
- A square number never ends in 2, 3, 7 or 8.
- Squares of whole tens end in two zeros: 10 × 10 = 100, 20 × 20 = 400.
Is 36 a square number?
- Look for a number that times itself gives 36.
- 5 × 5 = 25 is too small; 6 × 6 = 36.
Answer: Yes, 36 = 6 × 6.
Is 50 a square number?
- 7 × 7 = 49 and 8 × 8 = 64.
- 50 lies between them, so no whole number times itself makes 50.
Answer: No.
Examples
8 × 8 = ?
9 × 9 = ?
Practice problems with answers
Solve these problems on paper or out loud, then check the answer key. The online practice and the printable worksheet give a new set every time.
- 10 × 10 = ___
- 9 × 9 = ___
- 4 × 4 = ___
- 3 × 3 = ___
- 2 × 2 = ___
- 11 × 11 = ___
- 6 × 6 = ___
- 12 × 12 = ___
Show answers
- 100
- 81
- 16
- 9
- 4
- 121
- 36
- 144
Common mistakes
- Mixing up "squared" and "times two": 6² is 6 × 6 = 36, not 12.
- Thinking every even number is a square: 8, 10 and 12 are not.
- Guessing instead of checking with a multiplication or a dot picture.
Questions parents ask
What are the square numbers from 1 to 100?
There are ten: 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100.
Is 1 a square number?
Yes. 1 × 1 = 1; a single dot is the smallest square.
How do square numbers help with the times tables?
They run along the diagonal of the multiplication chart. A child who knows 6 × 6 = 36 gets 6 × 7 by adding one more 6: 42.
Times Divide
Multiplication and division worksheets that follow what the child has already solved.
The app does not generate PDF sheets at random. It uses the child’s previous results, including offline sheets, so the next practice can focus on what still needs work.
- Generate printable PDFs from the child’s history.
- Enter solved offline sheets quickly after practice.
- The app shows each answer; you mark it correct or not.
Scan with a phone to open Google Play