Table of Contents

**Cube Root formula of Perfect Cubes from 1 to 1**00

**How to find ****the cube**** root of a number quickly | Cube Root Calculator**

The *cube root* of a number means it is a value of that, when used in multiplication by itself in **three times**, gives that number.

In this page explained about one simple and easy tip for finding **Cube Roots of Perfect Cubes of two digits numbers**. By this *cube root formula*, we find cube root in a fraction of seconds.__These points to be remembered for this cube root formula.__

- The given number should be perfect two digit cube.
- Remember cubes of 1 to 10 numbers.
- As per the cubes identify as follow as below table.

1^{3} = 1 | If last a digit of perfect cube number =1,
last a digit of cube root for that number=1 |

2^{3} = 8 | If last a digit of perfect cube number =8,
last a digit of cube root for that number=2 |

3^{3} = 27 | If last a digit of perfect cube number =7,
last a digit of cube root for that number=3 |

4^{3} = 64 | If last a digit of perfect cube number =4,
last a digit of cube root for that number=4 |

5^{3} = 125 | If last a digit of perfect cube number =5,
last a digit of cube root for that number=5 |

6^{3} = 216 | If last a digit of perfect cube number =6,
last a digit of cube root for that number=6 |

7^{3} = 343 | If last a digit of perfect cube number =3,
last a digit of cube root for that number=7 |

8^{3} =512 | If last a digit of perfect cube number =2,
last a digit of cube root for that number=8 |

9^{3} = 729 | If last a digit of perfect cube number =9,
last a digit of cube root for that number=9 |

10^{3} = 1000 | If last a digit of perfect cube number =0,
last digit of cube root for that number=0 |

If we put interest in *mathematics* then it is a very interesting subject and easy to learn. Now let’s see how we can easily find out cube roots of perfect cubes within a fraction of seconds.

Take examples to easily understand the **cube root formula****Example 1: Find Cube Root of 13824****Step 1**

Identify the last three digits from the right side and make a group of these three digits

i.e., 13 – 824**Step 2**

Take the last group which is 824. And then find the last digit of 824 is 4

According to the above table if the last digit having 4 then the last digit of cube root for that number is 4

Hence the rightmost digit of the cube root of the given number is 4**Step 3**

Take the next group which is 13

Find out the value of 13 lies in between the cube of the numbers 2^{3 }and 3^{3}

8 < 13 < 27

Take small cube number i.e “ 2 “

Hence the left neighbor digit of the answer is 2**So our answer = 24****Example 2: Find Cube Root of 175616****Step 1**

Identify the last three digits from the right side and make a group of these three digits

i.e., 176 – 616**Step 2**

Take the last group which is 616. And then find the last digit of 616 is 6

According to the above table if the last digit having 6 then the last digit of cube root for that number is 6

Hence the rightmost digit of the cube root of the given number is 6**Step 3**

Take the next group which is 176

Find out the 176 lies in between the cube of the numbers i.e 5^{3 }and 6^{3}

125 < 176 < 216

Take small cube number i.e “ 5 “

Hence the left neighbor digit of the answer is 5**So our answer = 56****Example 3: Find Cube Root of 804357****Step 1**

Identify the last three digits from the right side and make a group of these three digits

i.e., 804 – 357**Step 2**

Take the last group which is 357. And then find the last digit of 357 is 7

According to the above table if the last digit having 7 then the last digit of cube root for that number is 3

Hence the rightmost digit of the cube root of the given number is 3**Step 3**

Take the next group which is 804

Find out the 176 lies in between the cube of the numbers i.e 9^{3 }and 10^{3}

729 < 804 < 1000

Take small cube number i.e “ 9 “

Hence the left neighbor digit of the answer is 9**So our answer = 93****Example 4: Find Cube Root of 438976****Step 1**

Identify the last three digits from the right side and make a group of these three digits

i.e., 438 – 976**Step 2**

Take the last group which is 976. And then find the last digit of 976 is 6

According to the above table if the last digit having 6 then the last digit of cube root for that number is 6

Hence the rightmost digit of the cube root of the given number is 6**Step 3**

Take the next group which is 438

Find out the 438 lies in between the cube of the numbers i.e 7^{3 }and 8^{3}

343 < 438 < 512

Take small cube number i.e “ 7 “

Hence the left neighbor digit of the answer is 7

So our answer = 76

Friend, it is very cube root formula for perfect cubes. Once if we understand the logic we can answer easily within a fraction of seconds.

**Cube Root & Cubes of 1 to 100:**

Number | Cube | CubeRoot |
---|---|---|

1 | 1 | 1.000 |

2 | 8 | 1.260 |

3 | 27 | 1.442 |

4 | 64 | 1.587 |

5 | 125 | 1.710 |

6 | 216 | 1.817 |

7 | 343 | 1.913 |

8 | 512 | 2.000 |

9 | 729 | 2.080 |

10 | 1000 | 2.154 |

11 | 1331 | 2.224 |

12 | 1728 | 2.289 |

13 | 2197 | 2.351 |

14 | 2744 | 2.410 |

15 | 3375 | 2.466 |

16 | 4096 | 2.520 |

17 | 4913 | 2.571 |

18 | 5832 | 2.621 |

19 | 6859 | 2.668 |

20 | 8000 | 2.714 |

21 | 9261 | 2.759 |

22 | 10648 | 2.802 |

23 | 12167 | 2.844 |

24 | 13824 | 2.884 |

25 | 15625 | 2.924 |

26 | 17576 | 2.962 |

27 | 19683 | 3.000 |

28 | 21952 | 3.037 |

29 | 24389 | 3.072 |

30 | 27000 | 3.107 |

31 | 29791 | 3.141 |

32 | 32768 | 3.175 |

33 | 35937 | 3.208 |

34 | 39304 | 3.240 |

35 | 42875 | 3.271 |

36 | 46656 | 3.302 |

37 | 50653 | 3.332 |

38 | 54872 | 3.362 |

39 | 59319 | 3.391 |

40 | 64000 | 3.420 |

41 | 68921 | 3.448 |

42 | 74088 | 3.476 |

43 | 79507 | 3.503 |

44 | 85184 | 3.530 |

45 | 91125 | 3.557 |

46 | 97336 | 3.583 |

47 | 103823 | 3.609 |

48 | 110592 | 3.634 |

49 | 117649 | 3.659 |

50 | 125000 | 3.684 |

51 | 132651 | 3.708 |

52 | 140608 | 3.733 |

53 | 148877 | 3.756 |

54 | 157464 | 3.780 |

55 | 166375 | 3.803 |

56 | 175616 | 3.826 |

57 | 185193 | 3.849 |

58 | 195112 | 3.871 |

59 | 205379 | 3.893 |

60 | 216000 | 3.915 |

61 | 226981 | 3.936 |

62 | 238328 | 3.958 |

63 | 250047 | 3.979 |

64 | 262144 | 4.000 |

65 | 274625 | 4.021 |

66 | 287496 | 4.041 |

67 | 300763 | 4.062 |

68 | 314432 | 4.082 |

69 | 328509 | 4.102 |

70 | 343000 | 4.121 |

71 | 357911 | 4.141 |

72 | 373248 | 4.160 |

73 | 389017 | 4.179 |

74 | 405224 | 4.198 |

75 | 421875 | 4.217 |

76 | 438976 | 4.236 |

77 | 456533 | 4.254 |

78 | 474552 | 4.273 |

79 | 493039 | 4.291 |

80 | 512000 | 4.309 |

81 | 531441 | 4.327 |

82 | 551368 | 4.344 |

83 | 571787 | 4.362 |

84 | 592704 | 4.380 |

85 | 614125 | 4.397 |

86 | 636056 | 4.414 |

87 | 658503 | 4.431 |

88 | 681472 | 4.448 |

89 | 704969 | 4.465 |

90 | 729000 | 4.481 |

91 | 753571 | 4.498 |

92 | 778688 | 4.514 |

93 | 804357 | 4.531 |

94 | 830584 | 4.547 |

95 | 857375 | 4.563 |

96 | 884736 | 4.579 |

97 | 912673 | 4.595 |

98 | 941192 | 4.610 |

99 | 970299 | 4.626 |

100 | 1000000 | 4.642 |