# Square Numbers

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Square 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