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# Square numbers

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(Redirected from Perfect squares)

The **square numbers** (**perfect squares**, or just **squares**), are integers for which the square root is an integer. Each prime in the prime factorization of a square number appears an even number of times.

√ 144 = √ 2 4 ⋅ 3 2 = 2 2 ⋅ 3 1 = 12 |

√ 12 = √ 2 2 ⋅ 3 1 = 2 1 ⋅ √ 3 ≈ 3.464101615 |

A000290 The squares:

a (n) = n 2, n ≥ 0 |

- {0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, ...}

## Square numbers as figurate numbers

4-sided polygonal numbers.

2-dimensional regular orthotopic numbers.

2-dimensional orthoplicial polytopic numbers.

## See also

- Rational squares (rational numbers for which the square root is a rational number)