Squares and Square Roots 1 to 100 (Table)
The square of n is n x n, and its square root is the number that multiplies by itself to give n. From 1 to 100 there are exactly 10 perfect squares, and other roots show 4 decimal places.
Total Integers100numbers 1 to 100
Perfect Squares101, 4, 9, 16, 25, 36, 49, 64, 81, 100
Smallest Square1² = 1first perfect square
Largest Square100² = 10,000in this table
Core Formula & Rules
| Rule | What It Means | Example |
|---|---|---|
| Square | n² = n × n. | 12² = 12 × 12 = 144. |
| Square Root | √n is the number whose square is n, so (√n)² = n. For non-perfect squares it is shown up to 4 decimal places. | √49 = 7 and √2 = 1.4142. |
| Last Digit Rule | A perfect square never ends in 2, 3, 7 or 8. It can only end in 0, 1, 4, 5, 6 or 9. | 2209 ends in 9 and may be a square. 2207 ends in 7 and cannot be. |
| Odd Number Sum | The square of n equals the sum of the first n odd numbers. | 5² = 1 + 3 + 5 + 7 + 9 = 25. |
Example: 2^2 = 2 x 2 = 4
sqrt(2) = 1.4142
2 is not a perfect square. It lies between 1^2 = 1 and 2^2 = 4.
Perfect Square: No| Number (n) | Square (n²) | Square Root (√n) | Perfect Square? | Last Digit Pattern (n → n²) | Copy |
|---|---|---|---|---|---|
| Numbers 1 to 25 | |||||
| 1 | 1 | 1 | Yes | 1 → 1 | |
| 2 | 4 | 1.4142 | No | 2 → 4 | |
| 3 | 9 | 1.7321 | No | 3 → 9 | |
| 4 | 16 | 2 | Yes | 4 → 6 | |
| 5 | 25 | 2.2361 | No | 5 → 5 | |
| 6 | 36 | 2.4495 | No | 6 → 6 | |
| 7 | 49 | 2.6458 | No | 7 → 9 | |
| 8 | 64 | 2.8284 | No | 8 → 4 | |
| 9 | 81 | 3 | Yes | 9 → 1 | |
| 10 | 100 | 3.1623 | No | 0 → 0 | |
| 11 | 121 | 3.3166 | No | 1 → 1 | |
| 12 | 144 | 3.4641 | No | 2 → 4 | |
| 13 | 169 | 3.6056 | No | 3 → 9 | |
| 14 | 196 | 3.7417 | No | 4 → 6 | |
| 15 | 225 | 3.8730 | No | 5 → 5 | |
| 16 | 256 | 4 | Yes | 6 → 6 | |
| 17 | 289 | 4.1231 | No | 7 → 9 | |
| 18 | 324 | 4.2426 | No | 8 → 4 | |
| 19 | 361 | 4.3589 | No | 9 → 1 | |
| 20 | 400 | 4.4721 | No | 0 → 0 | |
| 21 | 441 | 4.5826 | No | 1 → 1 | |
| 22 | 484 | 4.6904 | No | 2 → 4 | |
| 23 | 529 | 4.7958 | No | 3 → 9 | |
| 24 | 576 | 4.8990 | No | 4 → 6 | |
| 25 | 625 | 5 | Yes | 5 → 5 | |
| Numbers 26 to 50 | |||||
| 26 | 676 | 5.0990 | No | 6 → 6 | |
| 27 | 729 | 5.1962 | No | 7 → 9 | |
| 28 | 784 | 5.2915 | No | 8 → 4 | |
| 29 | 841 | 5.3852 | No | 9 → 1 | |
| 30 | 900 | 5.4772 | No | 0 → 0 | |
| 31 | 961 | 5.5678 | No | 1 → 1 | |
| 32 | 1024 | 5.6569 | No | 2 → 4 | |
| 33 | 1089 | 5.7446 | No | 3 → 9 | |
| 34 | 1156 | 5.8310 | No | 4 → 6 | |
| 35 | 1225 | 5.9161 | No | 5 → 5 | |
| 36 | 1296 | 6 | Yes | 6 → 6 | |
| 37 | 1369 | 6.0828 | No | 7 → 9 | |
| 38 | 1444 | 6.1644 | No | 8 → 4 | |
| 39 | 1521 | 6.2450 | No | 9 → 1 | |
| 40 | 1600 | 6.3246 | No | 0 → 0 | |
| 41 | 1681 | 6.4031 | No | 1 → 1 | |
| 42 | 1764 | 6.4807 | No | 2 → 4 | |
| 43 | 1849 | 6.5574 | No | 3 → 9 | |
| 44 | 1936 | 6.6332 | No | 4 → 6 | |
| 45 | 2025 | 6.7082 | No | 5 → 5 | |
| 46 | 2116 | 6.7823 | No | 6 → 6 | |
| 47 | 2209 | 6.8557 | No | 7 → 9 | |
| 48 | 2304 | 6.9282 | No | 8 → 4 | |
| 49 | 2401 | 7 | Yes | 9 → 1 | |
| 50 | 2500 | 7.0711 | No | 0 → 0 | |
| Numbers 51 to 75 | |||||
| 51 | 2601 | 7.1414 | No | 1 → 1 | |
| 52 | 2704 | 7.2111 | No | 2 → 4 | |
| 53 | 2809 | 7.2801 | No | 3 → 9 | |
| 54 | 2916 | 7.3485 | No | 4 → 6 | |
| 55 | 3025 | 7.4162 | No | 5 → 5 | |
| 56 | 3136 | 7.4833 | No | 6 → 6 | |
| 57 | 3249 | 7.5498 | No | 7 → 9 | |
| 58 | 3364 | 7.6158 | No | 8 → 4 | |
| 59 | 3481 | 7.6811 | No | 9 → 1 | |
| 60 | 3600 | 7.7460 | No | 0 → 0 | |
| 61 | 3721 | 7.8102 | No | 1 → 1 | |
| 62 | 3844 | 7.8740 | No | 2 → 4 | |
| 63 | 3969 | 7.9373 | No | 3 → 9 | |
| 64 | 4096 | 8 | Yes | 4 → 6 | |
| 65 | 4225 | 8.0623 | No | 5 → 5 | |
| 66 | 4356 | 8.1240 | No | 6 → 6 | |
| 67 | 4489 | 8.1854 | No | 7 → 9 | |
| 68 | 4624 | 8.2462 | No | 8 → 4 | |
| 69 | 4761 | 8.3066 | No | 9 → 1 | |
| 70 | 4900 | 8.3666 | No | 0 → 0 | |
| 71 | 5041 | 8.4261 | No | 1 → 1 | |
| 72 | 5184 | 8.4853 | No | 2 → 4 | |
| 73 | 5329 | 8.5440 | No | 3 → 9 | |
| 74 | 5476 | 8.6023 | No | 4 → 6 | |
| 75 | 5625 | 8.6603 | No | 5 → 5 | |
| Numbers 76 to 100 | |||||
| 76 | 5776 | 8.7178 | No | 6 → 6 | |
| 77 | 5929 | 8.7750 | No | 7 → 9 | |
| 78 | 6084 | 8.8318 | No | 8 → 4 | |
| 79 | 6241 | 8.8882 | No | 9 → 1 | |
| 80 | 6400 | 8.9443 | No | 0 → 0 | |
| 81 | 6561 | 9 | Yes | 1 → 1 | |
| 82 | 6724 | 9.0554 | No | 2 → 4 | |
| 83 | 6889 | 9.1104 | No | 3 → 9 | |
| 84 | 7056 | 9.1652 | No | 4 → 6 | |
| 85 | 7225 | 9.2195 | No | 5 → 5 | |
| 86 | 7396 | 9.2736 | No | 6 → 6 | |
| 87 | 7569 | 9.3274 | No | 7 → 9 | |
| 88 | 7744 | 9.3808 | No | 8 → 4 | |
| 89 | 7921 | 9.4340 | No | 9 → 1 | |
| 90 | 8100 | 9.4868 | No | 0 → 0 | |
| 91 | 8281 | 9.5394 | No | 1 → 1 | |
| 92 | 8464 | 9.5917 | No | 2 → 4 | |
| 93 | 8649 | 9.6437 | No | 3 → 9 | |
| 94 | 8836 | 9.6954 | No | 4 → 6 | |
| 95 | 9025 | 9.7468 | No | 5 → 5 | |
| 96 | 9216 | 9.7980 | No | 6 → 6 | |
| 97 | 9409 | 9.8489 | No | 7 → 9 | |
| 98 | 9604 | 9.8995 | No | 8 → 4 | |
| 99 | 9801 | 9.9499 | No | 9 → 1 | |
| 100 | 10000 | 10 | Yes | 0 → 0 | |
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Frequently Asked Questions
| Question | Answer |
|---|---|
| What is a perfect square? | A perfect square is the square of a whole number. There are 10 perfect squares from 1 to 100: 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100. |
| What is the square root of 2? | The square root of 2 is 1.4142 when rounded to 4 decimal places. |
| Which digits can a perfect square end in? | A perfect square can only end in 0, 1, 4, 5, 6 or 9. It never ends in 2, 3, 7 or 8. |
| What is 100 squared? | 100 squared is 10,000, because 100 x 100 = 10,000. |
| How do you find the square of a number? | Multiply the number by itself: n^2 = n x n. For example, 12 squared is 12 x 12 = 144. |
| Is the square root of a non-perfect square exact? | No. The square root of a number that is not a perfect square is irrational, so its decimal never ends or repeats. Tables round it, for example the square root of 3 is about 1.7321. |
Related Number Theory References
| Related Page | What You Will Find |
|---|---|
| Multiples of Numbers (1-100) | The first 10 multiples of every number from 1 to 100. |
| Factors of Numbers (1-100) | All factors, factor count and sum of factors for every number from 1 to 100. |
| Prime Factorization Table (1-100) | Prime factors and exponential form for every number from 1 to 100. |
| Prime Numbers (1-1000) | All 168 primes up to 1000 with a prime checker and distribution table. |