50 cards

Perfect Squares Flashcards

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9²

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How to practise

Next step Drill every times table fact, 1 to 12

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Squares 1² to 12² 12

1² 1 × 1 = 1. One times itself is still one.
2² 2 × 2 = 4. That is 1 + 3: the square before, plus the next odd number.
3² 3 × 3 = 9. That is 4 + 5: the square before, plus the next odd number.
4² 4 × 4 = 16. That is 9 + 7: the square before, plus the next odd number.
5² 5 × 5 = 25. That is 16 + 9: the square before, plus the next odd number.
6² 6 × 6 = 36. That is 25 + 11: the square before, plus the next odd number.
7² 7 × 7 = 49. That is 36 + 13: the square before, plus the next odd number.
8² 8 × 8 = 64. That is 49 + 15: the square before, plus the next odd number.
9² 9 × 9 = 81. That is 64 + 17: the square before, plus the next odd number.
10² 10 × 10 = 100. That is 81 + 19: the square before, plus the next odd number.
11² 11 × 11 = 121. That is 100 + 21: the square before, plus the next odd number.
12² 12 × 12 = 144. That is 121 + 23: the square before, plus the next odd number.

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Squares 13² to 25² 13

13² 13 × 13 = 169. That is 144 + 25: the square before, plus the next odd number.
14² 14 × 14 = 196. That is 169 + 27: the square before, plus the next odd number.
15² 15 × 15 = 225. That is 196 + 29: the square before, plus the next odd number.
16² 16 × 16 = 256. That is 225 + 31: the square before, plus the next odd number.
17² 17 × 17 = 289. That is 256 + 33: the square before, plus the next odd number.
18² 18 × 18 = 324. That is 289 + 35: the square before, plus the next odd number.
19² 19 × 19 = 361. That is 324 + 37: the square before, plus the next odd number.
20² 20 × 20 = 400. That is 361 + 39: the square before, plus the next odd number.
21² 21 × 21 = 441. That is 400 + 41: the square before, plus the next odd number.
22² 22 × 22 = 484. That is 441 + 43: the square before, plus the next odd number.
23² 23 × 23 = 529. That is 484 + 45: the square before, plus the next odd number.
24² 24 × 24 = 576. That is 529 + 47: the square before, plus the next odd number.
25² 25 × 25 = 625. That is 576 + 49: the square before, plus the next odd number.

Roots √1 to √144 12

√1 1, because 1 × 1 = 1. A square that ends in 1 has a root that ends in 1 or 9.
√4 2, because 2 × 2 = 4. A square that ends in 4 has a root that ends in 2 or 8.
√9 3, because 3 × 3 = 9. A square that ends in 9 has a root that ends in 3 or 7.
√16 4, because 4 × 4 = 16. A square that ends in 6 has a root that ends in 4 or 6.
√25 5, because 5 × 5 = 25. A square that ends in 5 has a root that ends in 5.
√36 6, because 6 × 6 = 36. A square that ends in 6 has a root that ends in 4 or 6.
√49 7, because 7 × 7 = 49. A square that ends in 9 has a root that ends in 3 or 7.
√64 8, because 8 × 8 = 64. A square that ends in 4 has a root that ends in 2 or 8.
√81 9, because 9 × 9 = 81. A square that ends in 1 has a root that ends in 1 or 9.
√100 10, because 10 × 10 = 100. A square that ends in 0 has a root that ends in 0.
√121 11, because 11 × 11 = 121. A square that ends in 1 has a root that ends in 1 or 9.
√144 12, because 12 × 12 = 144. A square that ends in 4 has a root that ends in 2 or 8.

Roots √169 to √625 13

√169 13, because 13 × 13 = 169. A square that ends in 9 has a root that ends in 3 or 7.
√196 14, because 14 × 14 = 196. A square that ends in 6 has a root that ends in 4 or 6.
√225 15, because 15 × 15 = 225. A square that ends in 5 has a root that ends in 5.
√256 16, because 16 × 16 = 256. A square that ends in 6 has a root that ends in 4 or 6.
√289 17, because 17 × 17 = 289. A square that ends in 9 has a root that ends in 3 or 7.
√324 18, because 18 × 18 = 324. A square that ends in 4 has a root that ends in 2 or 8.
√361 19, because 19 × 19 = 361. A square that ends in 1 has a root that ends in 1 or 9.
√400 20, because 20 × 20 = 400. A square that ends in 0 has a root that ends in 0.
√441 21, because 21 × 21 = 441. A square that ends in 1 has a root that ends in 1 or 9.
√484 22, because 22 × 22 = 484. A square that ends in 4 has a root that ends in 2 or 8.
√529 23, because 23 × 23 = 529. A square that ends in 9 has a root that ends in 3 or 7.
√576 24, because 24 × 24 = 576. A square that ends in 6 has a root that ends in 4 or 6.
√625 25, because 25 × 25 = 625. A square that ends in 5 has a root that ends in 5.

How this list was compiled: Arithmetic, worked twice on 2026-10-09: every square by multiplying and again as the sum of the first odd numbers, every root by taking the whole-number root and squaring it back. What a square number is, why it is called square, each square as the one before plus an odd number, the last digits a square can have and 0 as a square: https://en.wikipedia.org/wiki/Square_number, read 2026-10-09. Licence: own work

How it works

These perfect squares flashcards put a square such as 7² on the front and 49 on the back, from 1² to 25². A second deck turns each fact around and asks the square root: √49 on the front, 7 on the back.

Read the full guide

What is on the perfect square flashcards

Squares 1² to 12² are the twelve on the diagonal of a times table chart. Squares 13² to 25² run from 169 to 625. The two root sets ask the same facts backward, √1 to √144 and √169 to √625. Every back shows the working, such as 7 × 7 = 49.

Print the perfect squares flash cards

Pick a set, turn a card, then press the print button under it: 12 cards to a sheet of Letter or A4. A set that stops at 12 is one sheet, a set from 13 to 25 puts its last card on a second, and all 50 cards take 5. Print double-sided, flipped on the long edge, and 49 lands behind 7².

Each square is the one before plus the next odd number: 16 + 9 = 25. The backs show the step.
No perfect square ends in 2, 3, 7 or 8, so 152 and 283 cannot be one.
A number that ends in 5 has a square that ends in 25: 15² is 225 and 25² is 625.

Questions and answers

What is a perfect square?

A whole number times itself: 49 is a perfect square because 7 × 7 = 49. It is also called a square number, because that many dots can be set out in a square, 7 rows of 7.

What are the perfect squares from 1 to 25?

The squares of 1 to 25 are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576 and 625.

What is the square root of a perfect square?

The whole number that was multiplied by itself: √49 is 7 because 7 × 7 = 49. Only a perfect square has a whole-number root. √50 lies between 7 and 8.

Is 0 a perfect square?

Yes. 0 × 0 = 0, so 0 is a perfect square, and it comes before 1 in the list of square numbers. This deck starts at 1².