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Square NumbersSquare numbers are numbers that that are the product of one integer with itself. The term "perfect square" is also used. For example, 9 and 16 are perfect squares because 9 = 3 × 3 and 16 = 4 × 4. These could also be written using exponents; for example, 16 = 4² (pronounced "four squared").
Square numbers were named by the ancient Greeks, who also named various other classifications for numbers, such as triangular numbers, prime numbers, composite numbers, perfect numbers, deficient, abundant, amicable, and so on. They are called "squares" because they can represent the area of a square with integer side lengths. Another way to look at is that a square number of counters can be arranged to form a square.
Here is a table of the first 50 square numbers:
| 1² | = | 1 |
| 2² | = | 4 |
| 3² | = | 9 |
| 4² | = | 16 |
| 5² | = | 25 |
| 6² | = | 36 |
| 7² | = | 49 |
| 8² | = | 64 |
| 9² | = | 81 |
| 10² | = | 100 |
| 11² | = | 121 |
| 12² | = | 144 |
| 13² | = | 169 |
| 14² | = | 196 |
| 15² | = | 225 |
| 16² | = | 256 |
| 17² | = | 289 |
| 18² | = | 324 |
| 19² | = | 361 |
| 20² | = | 400 |
| 21² | = | 441 |
| 22² | = | 484 |
| 23² | = | 529 |
| 24² | = | 576 |
| 25² | = | 625 |
| 26² | = | 676 |
| 27² | = | 729 |
| 28² | = | 784 |
| 29² | = | 841 |
| 30² | = | 900 |
| 31² | = | 961 |
| 32² | = | 1024 |
| 33² | = | 1089 |
| 34² | = | 1156 |
| 35² | = | 1225 |
| 36² | = | 1296 |
| 37² | = | 1369 |
| 38² | = | 1444 |
| 39² | = | 1521 |
| 40² | = | 1600 |
| 41² | = | 1681 |
| 42² | = | 1764 |
| 43² | = | 1849 |
| 44² | = | 1936 |
| 45² | = | 2025 |
| 46² | = | 2116 |
| 47² | = | 2209 |
| 48² | = | 2304 |
| 49² | = | 2401 |
| 50² | = | 2500 |