# Square Root : Find square Root of any number in a 5 seconds

*Square number*

A *square number* or perfect square is the product of some integer with itself. For example, 25 is a square number, since it can be written as 5 × 5.

*How to find Square of a Number*

To Find square of a number, just multiply it by itself.

For Example, square of 2 is 2 x 2 = 4

*Square Root*

The square root of a number is a value that, when multiplied by itself, gives the number.

*Square Root Symbol*

The symbol of Square root is √

*Finding Square Roots*

The easiest way to find a square root is to use a calculator, but you can do it without one. Here’s one way, using 12 as an example of the squared number:

✓ Pick a number that when squared, comes close to (but is less than) the number whose square root you’re finding: 3 x 3 = 9. This is a better choice than 4: 4 × 4 = 16

✓ Divide the number you’re finding the square root of (12) by the number you squared (3) in step 1: 12 ÷ 3 = 4

✓ Average the closest square root (3) and the answer of step 2 (4): 3 + 4 = 7. 7 ÷ 2 = 3.5

✓ Square the average to see how close the number is to 12:

3.5 × 3.5 = 12.25—Close, but not close enough!

Repeat steps 2 and 3 until the number squared is very close to 12:

Divide: 12 ÷ 3.5 = 3.43

Average: 3.5 + 3.43 = 6.935

6.935 ÷ 2 = 3.465

3.465 × 3.465 = 12.006, close enough!

*Problems based on Square Root*

**How to Calculate Square of a Number**

**Example1:** 6 × 6 = 36, so a square root of 36 is 6.

**Example2:** √25 = 5 (because 5 x 5 = 25)

**Example3:** √9 = 3 (because 3 x 3 = 9 )

**Example 4:** √256 = 16 (because 16 x 16 = 256 )

**Example 5:** √2500 = 50 (because 50 x 50 = 2500)

**Example 6:** √3025 = 55 (because 55 x 55 = 3025)

**Example 7:** √4489 = 67 (because 67 x 67 = 4489)

**Example 8:** √7744 = 88 (because 88 x 88 = 7744)

**Example 9:** √8649 = 93 (because 93 x 93 = 8649)

**Example 10:** √10000 = 100 (because 100 x 100 = 10000)

**Note:**

1. We can also square negative numbers.

For Example (-3) X (-3)= 9

2. Square Root is also applied for decimals

For Example √15.5 = 3.94

## Perfect Square

A number made by squaring a whole number (0,1,2,3,4_ _ _ _)

For Example 9 is a perfect square because it can be expressed as 3 x 3 (the product of two equal integers)

16 is a perfect square because it can be expressed as 4 * 4 (the product of two equal integers)

*Square roots of numbers 1-100*

Given below are the square numbers up to 100

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 |

*Find Square Root Quickly*

*Watch the video below to learn some quick tricks for calculation of square root.*