# List of Square Roots and Cube Roots from 1 to 100

Understanding the concepts of square roots and cube roots is essential for mastering mathematics. In this comprehensive guide, we will explore the list of square roots and cube roots from 1 to 100 while delving into their properties and methods for calculating them. Additionally, we will provide examples, explanations, and a complete list of square roots and cube roots for easy reference.

## Square Roots and Cube Roots

Before diving into the list of square roots and cube roots, let’s briefly discuss the definitions and symbols of these mathematical concepts.

### Square Root

A square root is a special number. When you multiply it by itself, you get the original number back. In other words, the square root of a number x is the number that, when squared, equals x.

Example:

√4 = √(2 × 2) = 2

### Cube Root

A cube root is a number that, when multiplied by itself three times, results in the original number. Essentially, the cube root of a number y is the number that, when cubed, equals y.

Example:

∛27 = ∛(3 × 3 × 3) = 3

Now that we have a basic understanding of square roots and cube roots, let’s explore the complete list of square roots and cube roots from 1 to 100.

## List of Square Roots from 1 to 100

Below is a table containing the list of square roots for the numbers 1 to 100. This list can be a handy reference when solving mathematical problems involving square roots.

Number (N) | Square root (√N) |

1 | 1.000 |

2 | 1.414 |

3 | 1.732 |

4 | 2.000 |

5 | 2.236 |

6 | 2.449 |

7 | 2.646 |

8 | 2.828 |

9 | 3.000 |

10 | 3.162 |

11 | 3.317 |

12 | 3.464 |

13 | 3.606 |

14 | 3.742 |

15 | 3.873 |

16 | 4.000 |

17 | 4.123 |

18 | 4.243 |

19 | 4.359 |

20 | 4.472 |

21 | 4.583 |

22 | 4.690 |

23 | 4.796 |

24 | 4.899 |

25 | 5.000 |

26 | 5.099 |

27 | 5.196 |

28 | 5.292 |

29 | 5.385 |

30 | 5.477 |

31 | 5.568 |

32 | 5.657 |

33 | 5.745 |

34 | 5.831 |

35 | 5.916 |

36 | 6.000 |

37 | 6.083 |

38 | 6.164 |

39 | 6.245 |

40 | 6.325 |

41 | 6.403 |

42 | 6.481 |

43 | 6.557 |

44 | 6.633 |

45 | 6.708 |

46 | 6.782 |

47 | 6.856 |

48 | 6.928 |

49 | 7.000 |

50 | 7.071 |

51 | 7.141 |

52 | 7.211 |

53 | 7.280 |

54 | 7.348 |

55 | 7.416 |

56 | 7.483 |

57 | 7.550 |

58 | 7.616 |

59 | 7.681 |

60 | 7.746 |

61 | 7.810 |

62 | 7.874 |

63 | 7.937 |

64 | 8.000 |

65 | 8.062 |

66 | 8.124 |

67 | 8.185 |

68 | 8.246 |

69 | 8.307 |

70 | 8.367 |

71 | 8.426 |

72 | 8.485 |

73 | 8.544 |

74 | 8.602 |

75 | 8.660 |

76 | 8.718 |

77 | 8.775 |

78 | 8.832 |

79 | 8.888 |

80 | 8.944 |

81 | 9.000 |

82 | 9.055 |

83 | 9.110 |

84 | 9.165 |

85 | 9.220 |

86 | 9.274 |

87 | 9.327 |

88 | 9.381 |

89 | 9.434 |

90 | 9.487 |

91 | 9.539 |

92 | 9.592 |

93 | 9.644 |

94 | 9.695 |

95 | 9.747 |

96 | 9.798 |

97 | 9.849 |

98 | 9.899 |

99 | 9.950 |

100 | 10.000 |

## List of Cube Roots from 1 to 100

Similarly, here is a table containing the list of cube roots for the numbers 1 to 100. This list can be a useful reference when working with mathematical problems involving cube roots.

Number | Cube Root (^{3}√) |

1 | 1.000 |

2 | 1.260 |

3 | 1.442 |

4 | 1.587 |

5 | 1.710 |

6 | 1.817 |

7 | 1.913 |

8 | 2.000 |

9 | 2.080 |

10 | 2.154 |

11 | 2.224 |

12 | 2.289 |

13 | 2.351 |

14 | 2.410 |

15 | 2.466 |

16 | 2.520 |

17 | 2.571 |

18 | 2.621 |

19 | 2.668 |

20 | 2.714 |

21 | 2.759 |

22 | 2.802 |

23 | 2.844 |

24 | 2.884 |

25 | 2.924 |

26 | 2.962 |

27 | 3.000 |

28 | 3.037 |

29 | 3.072 |

30 | 3.107 |

31 | 3.141 |

32 | 3.175 |

33 | 3.208 |

34 | 3.240 |

35 | 3.271 |

36 | 3.302 |

37 | 3.332 |

38 | 3.362 |

39 | 3.391 |

40 | 3.420 |

41 | 3.448 |

42 | 3.476 |

43 | 3.503 |

44 | 3.530 |

45 | 3.557 |

46 | 3.583 |

47 | 3.609 |

48 | 3.634 |

49 | 3.659 |

50 | 3.684 |

51 | 3.708 |

52 | 3.733 |

53 | 3.756 |

54 | 3.780 |

55 | 3.803 |

56 | 3.826 |

57 | 3.849 |

58 | 3.871 |

59 | 3.893 |

60 | 3.915 |

61 | 3.936 |

62 | 3.958 |

63 | 3.979 |

64 | 4.000 |

65 | 4.021 |

66 | 4.041 |

67 | 4.062 |

68 | 4.082 |

69 | 4.102 |

70 | 4.121 |

71 | 4.141 |

72 | 4.160 |

73 | 4.179 |

74 | 4.198 |

75 | 4.217 |

76 | 4.236 |

77 | 4.254 |

78 | 4.273 |

79 | 4.291 |

80 | 4.309 |

81 | 4.327 |

82 | 4.344 |

83 | 4.362 |

84 | 4.380 |

85 | 4.397 |

86 | 4.414 |

87 | 4.431 |

88 | 4.448 |

89 | 4.465 |

90 | 4.481 |

91 | 4.498 |

92 | 4.514 |

93 | 4.531 |

94 | 4.547 |

95 | 4.563 |

96 | 4.579 |

97 | 4.595 |

98 | 4.610 |

99 | 4.626 |

100 | 4.642 |

## Properties of Square Roots

There are several properties of square roots that are important to understand when working with them. These properties include:

- If the unit digit of a number is 2, 3, 7, or 8, then its square root is not a natural number.
- If a number ends in an odd number of zeros, then its square root is not a natural number.
- When you find the square root of an even number, the answer will also be an even number. And when you find the square root of an odd number, the answer will also be an odd number.
- Negative numbers have no square roots in the set of real numbers.

## Properties of Cube Roots

Similar to square roots, there are several properties of cube roots that are essential to comprehend:

- The cube root of all odd numbers is an odd number. For example: ∛27 = 3, ∛729 = 9.
- The cube root of all even natural numbers is even. For example: ∛64 = 4, ∛512 = 8.
- When you find the cube root of a negative number, the answer will always be a negative number.

## Methods of Finding Square Roots and Cube Roots

While memorizing the list of square roots and cube roots from 1 to 15 can help solve problems quickly, there are two primary methods for calculating square roots and cube roots of more significant numbers:

- Prime Factorization Method
- Long Division Method

### Prime Factorization Method

The prime factorization method involves breaking down a number into its prime factors and then grouping similar factors to determine the square root or cube root.

#### Example: Square Root of 16

- Find the prime factors of 16:

2 × 2 × 2 × 2 - Group the factors: (2 × 2)²
- Take the square root: √16 = 4

#### Example: Cube Root of 64

- Find the prime factors of 64:

2 × 2 × 2 × 2 × 2 × 2 - Group the factors: (2 × 2)³
- Take the cube root: ∛64 = 8

### Long Division Method

The long division method is an alternative approach for calculating square roots and cube roots. This method involves dividing the given number by its factors repeatedly until the desired root is obtained.

#### Example: Cube Root of 729

Divide 729 by 3: 243

Divide 243 by 3: 81

Divide 81 by 3: 27

Divide 27 by 3: 9

Divide 9 by 3: 3

The cube root of 729 is 9

## Conclusion

Understanding the list of square roots, and cube roots, their properties, and methods for calculating them is crucial for success in mathematics. By using the provided tables and examples in this guide, you can master these concepts and improve your problem-solving skills. Remember to practice regularly and refer to the complete list of square roots and cube roots for quick reference when needed.