# Table of Squares and Square Roots

## What are square roots and why do we care?

The square root of a number is a number that, when multiplied by itself, equals the desired value. So, for example, the square root of 49 is 7 (7x7=49). The process of multiplying a number times itself is called **squaring**.

Numbers whose square roots are whole numbers, (or more accurately positive integers) are called perfect square numbers. Numbers with decimals aren't perfect square roots.

All positive numbers will have a positive number as their square root, called the principal, and a negative number. These numbers are all known as real numbers.

All negative numbers will have a complex number as their square root. A complex number is a number multiplied by *i. i *is the "imaginary" square root of -1. It's called imaginary, but it does exist to mathematicians.

### How do we write out square roots?

A square root equation is written out using a radical sign or radical symbol (√). The number that we want to get the root of comes after or under the tail of the radical (for example √3 if we wanted to find the square root of 3). The number after the radical is called the radicand. On a calculator, instead of the radical, you might see "sqrt".

### What do we use square roots for?

It may be a bit hard to picture it, but square roots are some of the most useful numbers around. Square root functions are super important for physics equations of all kinds. They're also valuable for statistics; statisticians use square roots all the time in analyzing the correlation between different points of data.

### List of Perfect Squares

Use this table to find the squares and square roots of numbers from **1** to **100**.

You can also use this table to estimate the square roots of larger numbers.

- For instance, if you want to find the square root of
**2000**, look in the**middle**column until you find the number that is closest to 2000. The number in the middle column that is closest to 2000 is**2,025**. - Now look in at the number to the
**left of 2,025**to find its square root. The square root of 2,025 is**45**. - Therefore,
**the approximate square root of 2,000 is 45**.

To get a more exact number, you will have to use a **calculator** (44.721 is the more exact square root of 2,000).

NUMBER | SQUARE | SQUARE ROOT |

1 | 1 | 1.000 |

2 | 4 | 1.414 |

3 | 9 | 1.732 |

4 | 16 | 2.000 |

5 | 25 | 2.236 |

6 | 36 | 2.449 |

7 | 49 | 2.646 |

8 | 64 | 2.828 |

9 | 81 | 3.000 |

10 | 100 | 3.162 |

11 | 121 | 3.317 |

12 | 144 | 3.464 |

13 | 169 | 3.606 |

14 | 196 | 3.742 |

15 | 225 | 3.873 |

16 | 256 | 4.000 |

17 | 289 | 4.123 |

18 | 324 | 4.243 |

19 | 361 | 4.359 |

20 | 400 | 4.472 |

21 | 441 | 4.583 |

22 | 484 | 4.690 |

23 | 529 | 4.796 |

24 | 576 | 4.899 |

25 | 625 | 5.000 |

26 | 676 | 5.099 |

27 | 729 | 5.196 |

28 | 784 | 5.292 |

29 | 841 | 5.385 |

30 | 900 | 5.477 |

31 | 961 | 5.568 |

32 | 1,024 | 5.657 |

33 | 1,089 | 5.745 |

34 | 1,156 | 5.831 |

35 | 1,225 | 5.916 |

36 | 1,296 | 6.000 |

37 | 1,369 | 6.083 |

38 | 1,444 | 6.164 |

39 | 1,521 | 6.245 |

40 | 1,600 | 6.325 |

41 | 1,681 | 6.403 |

42 | 1,764 | 6.481 |

43 | 1,849 | 6.557 |

44 | 1,936 | 6.633 |

45 | 2,025 | 6.708 |

46 | 2,116 | 6.782 |

47 | 2,209 | 6.856 |

48 | 2,304 | 6.928 |

49 | 2,401 | 7.000 |

50 | 2,500 | 7.071 |

51 | 2,601 | 7.141 |

52 | 2,704 | 7.211 |

53 | 2,809 | 7.280 |

54 | 2,916 | 7.348 |

55 | 3,025 | 7.416 |

56 | 3,136 | 7.483 |

57 | 3,249 | 7.550 |

58 | 3,364 | 7.616 |

59 | 3,481 | 7.681 |

60 | 3,600 | 7.746 |

61 | 3,721 | 7.810 |

62 | 3,844 | 7.874 |

63 | 3,969 | 7.937 |

64 | 4,096 | 8.000 |

65 | 4,225 | 8.062 |

66 | 4,356 | 8.124 |

67 | 4,489 | 8.185 |

68 | 4,624 | 8.246 |

69 | 4,761 | 8.307 |

70 | 4,900 | 8.367 |

71 | 5,041 | 8.426 |

72 | 5,184 | 8.485 |

73 | 5,329 | 8.544 |

74 | 5,476 | 8.602 |

75 | 5,625 | 8.660 |

76 | 5,776 | 8.718 |

77 | 5,929 | 8.775 |

78 | 6,084 | 8.832 |

79 | 6,241 | 8.888 |

80 | 6,400 | 8.944 |

81 | 6,561 | 9.000 |

82 | 6,724 | 9.055 |

83 | 6,889 | 9.110 |

84 | 7,056 | 9.165 |

85 | 7,225 | 9.220 |

86 | 7,396 | 9.274 |

87 | 7,569 | 9.327 |

88 | 7,744 | 9.381 |

89 | 7,921 | 9.434 |

90 | 8,100 | 9.487 |

91 | 8,281 | 9.539 |

92 | 8,464 | 9.592 |

93 | 8,649 | 9.644 |

94 | 8,836 | 9.695 |

95 | 9,025 | 9.747 |

96 | 9,216 | 9.798 |

97 | 9,409 | 9.849 |

98 | 9,604 | 9.899 |

99 | 9,801 | 9.950 |

100 | 10,000 | 10.000 |

NOTE: Square roots in this table are rounded to the nearest thousandth.