In this article we are going to discuss

**square numbers**.

A couple of lines down you can find our calculator which can square any real number.

The terms

**square number**and

**perfect square**are synonym.

It’s called

*perfect*square because the number is the square of an integer (whole number).

±

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## Square Numbers Definition

A square number is the product of some integer with itself.Therefore, it is expressed as n

^{2}= n × n;

**n**is a

**whole number**.

As you can see, a square number is an

**exponentiation**involving the

**base n**and the

**exponent**2, sometimes written as n^2.

In other words, it means

**n to the power of 2**.

It follows from that that n can be positive or negative (If you square a negative number the result will be a positive), but usually the meaning is n > 0.

If n represents the length of a side, then n^2 expresses the area of the shape of a square with side length n.

This answers the question

*how do you square a number*?

### Square Numbers Formula

Every square number equals the sum of the first n odd numbers:Next, let’s look at some examples.

## Square Numbers Examples

- Example 1 – The square number of 3: 3 × 3 = 9.
- Example 2 – The square number of 4: 4 × 4 = 16.
- Example 3 – The square number of 12: 12 × 12 = 144.

^{2}is the square number, then n is the principal square root.

- Example 4: The square root of 169 (13 × 13) is +/− 13.

If the square root is a whole number (has no decimal places), then the number is indeed a square number.

- Example 5: Is 18 a square number? No, √18 = ±4.2426406871 (has decimals).
- Example 6: Is 25 a square number? Yes, √25 = ±5 (has no decimals).
- Example 7: If the square of a number is y, then what is the original number x? By definition, the product y = x
^{2}, so x = √y.

Square of 3 | Square of 8 |

Square of 50 | Square of 125 |

Square of 64 | Square of 9 |

Square of 26 | Square of 16 |

Square of 48 | Square of 72 |

Square of 65 | Square of 52 |

Square of 80 | Square of 12 |

Square of 4 | Square of 11 |

## Frequently Asked Questions

### What is a Square Number?

A square number or perfect square is the result when a whole number has been multiplied by itself.

### How to Square Numbers in Excel?

To square a number n in Excel type n^2 or n*n.

### What is the Square of a Number?

The square of a number is the outcome of multiplying an integer by itself.

### How to Do Square Numbers?

You can square a number by means of exponentiation with base n and index 2, or you can multiply n × n.

### What Does Squared Mean in Math?

“Squared” is the past tense of the verb “to square”; in math it means that a number has been multiplied by itself.

### How to Square Numbers?

Take the decimal, fraction or whole number and multiply it by itself! Note that only if you square an integer do you get a perfect square.

### What is a Square Number of 100?

100^2 = 100 x 100 = 10,000.

### Is 18 a Perfect Square?

√18 = 4.2426406871 is not an integer, and as such 18 cannot be a perfect square.

### What Are the First 10 Square Numbers?

The first 10 square numbers are 0, 1, 4, 9, 16, 25, 36, 49, 64, 81.

### Why is 3 Not a Square Number?

A square number can not end in 2, 3, 7 and 8.

### What Is the Smallest Square Number?

The smallest square number is equal to 0.

### What Is the Easiest Way to Find a Square Number?

The easiest way to find a square number is multiplying a small, whole number by itself.

### Why is 20 Not a Square Number?

√20 = 4.4721359549 has digits and as such can not be a square number.

We are constantly trying to improve our site, and truly appreciate your feedback.

Ahead is the table in the context of this site.

## Square Numbers List

The table below contains the square numbers up to 100:Number | Square Number | Square Root |
---|---|---|

0 | 0 | 0 |

1 | 1 | +/− 1 |

2 | 4 | +/− 1.4142135624 |

3 | 9 | +/− 1.7320508076 |

4 | 16 | +/− 2 |

5 | 25 | +/− 2.2360679775 |

6 | 36 | +/− 2.4494897428 |

7 | 49 | +/− 2.6457513111 |

8 | 64 | +/− 2.8284271247 |

9 | 81 | +/− 3 |

10 | 100 | +/− 3.1622776602 |

11 | 121 | +/− 3.3166247904 |

12 | 144 | +/− 3.4641016151 |

13 | 169 | +/− 3.6055512755 |

14 | 196 | +/− 3.7416573868 |

15 | 225 | +/− 3.8729833462 |

16 | 256 | +/− 4 |

17 | 289 | +/− 4.1231056256 |

18 | 324 | +/− 4.2426406871 |

19 | 361 | +/− 4.3588989435 |

20 | 400 | +/− 4.472135955 |

21 | 441 | +/− 4.582575695 |

22 | 484 | +/− 4.6904157598 |

23 | 529 | +/− 4.7958315233 |

24 | 576 | +/− 4.8989794856 |

25 | 625 | +/− 5 |

26 | 676 | +/− 5.0990195136 |

27 | 729 | +/− 5.1961524227 |

28 | 784 | +/− 5.2915026221 |

29 | 841 | +/− 5.3851648071 |

30 | 900 | +/− 5.4772255751 |

31 | 961 | +/− 5.5677643628 |

32 | 1024 | +/− 5.6568542495 |

33 | 1089 | +/− 5.7445626465 |

34 | 1156 | +/− 5.8309518948 |

35 | 1225 | +/− 5.9160797831 |

36 | 1296 | +/− 6 |

37 | 1369 | +/− 6.0827625303 |

38 | 1444 | +/− 6.164414003 |

39 | 1521 | +/− 6.2449979984 |

40 | 1600 | +/− 6.3245553203 |

41 | 1681 | +/− 6.4031242374 |

42 | 1764 | +/− 6.4807406984 |

43 | 1849 | +/− 6.5574385243 |

44 | 1936 | +/− 6.6332495807 |

45 | 2025 | +/− 6.7082039325 |

46 | 2116 | +/− 6.7823299831 |

47 | 2209 | +/− 6.8556546004 |

48 | 2304 | +/− 6.9282032303 |

49 | 2401 | +/− 7 |

50 | 2500 | +/− 7.0710678119 |

51 | 2601 | +/− 7.1414284285 |

52 | 2704 | +/− 7.2111025509 |

53 | 2809 | +/− 7.2801098893 |

54 | 2916 | +/− 7.3484692283 |

55 | 3025 | +/− 7.4161984871 |

56 | 3136 | +/− 7.4833147735 |

57 | 3249 | +/− 7.5498344353 |

58 | 3364 | +/− 7.6157731059 |

59 | 3481 | +/− 7.6811457479 |

60 | 3600 | +/− 7.7459666924 |

61 | 3721 | +/− 7.8102496759 |

62 | 3844 | +/− 7.874007874 |

63 | 3969 | +/− 7.9372539332 |

64 | 4096 | +/− 8 |

65 | 4225 | +/− 8.0622577483 |

66 | 4356 | +/− 8.1240384046 |

67 | 4489 | +/− 8.1853527719 |

68 | 4624 | +/− 8.2462112512 |

69 | 4761 | +/− 8.3066238629 |

70 | 4900 | +/− 8.3666002653 |

71 | 5041 | +/− 8.4261497732 |

72 | 5184 | +/− 8.4852813742 |

73 | 5329 | +/− 8.5440037453 |

74 | 5476 | +/− 8.602325267 |

75 | 5625 | +/− 8.6602540378 |

76 | 5776 | +/− 8.7177978871 |

77 | 5929 | +/− 8.7749643874 |

78 | 6084 | +/− 8.8317608663 |

79 | 6241 | +/− 8.8881944173 |

80 | 6400 | +/− 8.94427191 |

81 | 6561 | +/− 9 |

82 | 6724 | +/− 9.0553851381 |

83 | 6889 | +/− 9.1104335791 |

84 | 7056 | +/− 9.1651513899 |

85 | 7225 | +/− 9.2195444573 |

86 | 7396 | +/− 9.2736184955 |

87 | 7569 | +/− 9.3273790531 |

88 | 7744 | +/− 9.3808315196 |

89 | 7921 | +/− 9.4339811321 |

90 | 8100 | +/− 9.4868329805 |

91 | 8281 | +/− 9.5393920142 |

92 | 8464 | +/− 9.5916630466 |

93 | 8649 | +/− 9.643650761 |

94 | 8836 | +/− 9.6953597148 |

95 | 9025 | +/− 9.7467943448 |

96 | 9216 | +/− 9.7979589711 |

97 | 9409 | +/− 9.8488578018 |

98 | 9604 | +/− 9.8994949366 |

99 | 9801 | +/− 9.9498743711 |

100 | 10000 | +/− 10 |

**sequence**of square numbers is 0 (0 x 0), 1 (1 x 1), 4 (2 x 2), 9 (3 x 3), 16 (4 x 4), 25 (5 x 5), 36 (6 x 6), 49 (7 x 7), 64 (8 x 8), 81 (9 x 9), …

## Square Numbers Calculator

Here we inform you that our tool at the top of this page works both ways; you can either fill in the upper or the lower input field.Our app works with all real numbers, and you don’t need to press a button unless you want to start over.

You may use the up and down arrows (called spinners) to increase or decrease the input value.

Frequently calculated terms include, for example: We now show you two recursive

**formulas**plus an identity which are sometimes useful to come up with n^2.

## Additional Information

In addition to the formula discussed above, any product n^{2}can be produced recursively:

- n
^{2}= (n − 1)^{2}+ (n − 1) + n = (n − 1)^{2}+ (2n − 1) - n
^{2}= 2 x (n − 1)^{2}− (n − 2)^{2}+ 2

- n
^{2}− (n − 1)^{2}= 2n − 1

- (2n)
^{2}= 4n^{2}

- (2n + 1) = 4(n
^{2}+ n) + 1

- In base 10, a square number cannot end in digits 2, 3, 7, 8.

Or simply consult our square numbers

**chart**.

Next is the summary of our article.

## Bottom Line

A**square number**

**n**means

^{2}**n × n**, n is an

**integer**and × is the multiplication symbol.

The exponentiation form n

^{2}or n^2 is mostly used to express a square number.

For a number to be a perfect square it’s last digit must be 0, 1, 4, 5, 6 or 9; else it is an imperfect square.

**If the second root of a squared number has no decimal places, then the squared number is a square number!**

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