# Squared

When a value is followed by the term "squared," it means that the value is being raised to the power of two. For example, two squared is written as follows:

In the above figure, "squared" refers to the exponent, 2.

Squaring a value (raising it to the power of 2) just means to multiply the number by itself: 2^{2} = 2 × 2 = 4. One way to visualize this is to use a square. Think of numerals as squares with side lengths of 1 unit, so 2 × 2 forms a square where each side is made up of 2 squares with 1 unit side lengths:

In this manner, we can see that a square with side lengths of 2 is comprised of 4 squares. This is one way to view the concept of area, and is why many measurements of area are "square units," such as ft^{2}, in^{2}, m^{2}, and more.

## Perfect squares

A perfect square is the square of an integer. It can be helpful to memorize perfect squares, at least up to a certain number, because it can allow us to more easily perform a lot of basic arithmetic. Below is a table showing the perfect squares from 0-20.

Integer | Squares |
---|---|

0 | 0 |

1 | 1 |

2 | 4 |

3 | 9 |

4 | 16 |

5 | 25 |

6 | 36 |

7 | 49 |

8 | 64 |

9 | 81 |

10 | 100 |

11 | 121 |

12 | 144 |

13 | 169 |

14 | 196 |

15 | 225 |

16 | 256 |

17 | 289 |

18 | 324 |

19 | 361 |

20 | 400 |

## Squares of negative numbers

The square of a number is always positive regardless of whether the number being squared is negative or positive. This is because a negative number multiplied by a negative number is positive, and a square is a number multiplied by itself, so the square of a negative number will always be positive.

This is important when solving algebraic equations that involve square roots.

Example

In this example, we know that x can be either -2 or 2, since the square of either is 4.