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Cube Root Formula

Cubes are an important part of the number system and are encountered frequently in arithmetic. Let us learn about the concept of cube root and the cube root formula in this article.

Cube Root Formula

The cube root formula is the inverse of the cube formula. In the cube formula, we multiply a number three times to get its cube, so in this case, we break down a number to be expressed as a product of three equal number and thus we get the cube root.

Cube Root Formula

Let us look into this with an example: What is the cube root of 1331?

  • The factors of 1728 are given as,
  • 1728 = 11 × 11 × 11
  • 3√1331 = 3√(11 × 11 × 11)
  • 3√1331 = 11

Another way to calculate the cube root is as follows using the below table is as follows:

13 = 1 If the last digit of perfect cube number =1, the last digit of cube root for that number=1
23 = 8 If the last digit of perfect cube number =8, the last digit of cube root for that number=2
33 = 27 If the last digit of perfect cube number =7, the last digit of cube root for that number=3
43 = 64 If the last digit of perfect cube number =4, the last digit of cube root for that number=4
53 = 125 If the last digit of perfect cube number =5, the last digit of cube root for that number=5
63 = 216 If the last digit of perfect cube number =6, the last digit of cube root for that number=6
73 = 343 If the last digit of perfect cube number =3, the last digit of cube root for that number=7
83 =512 If the last digit of perfect cube number =2, the last digit of cube root for that number=8
93 = 729 If the last digit of perfect cube number =9, the last digit of cube root for that number=9
103 = 1000 If the last digit of perfect cube number =0, last digit of cube root for that number=0

Let us now see how to use the table with the help of an example. So here, we will find the Cube Root of 13824 by using the following steps.

  • Step 1- Take the last three digits and make their group i.e., 13 – 824
  • Step 2 Take the last digit of the above group. As per the above table, if the last digit having 4 then the last digit of cube root for that number is 4. Hence the last digit of the cube root of the given number is 4
  • Step 3: Take the leftover part of the number which is 13. As per the above table, the value of 13 lies between 8 and 27 which are 23 and 33 respectively. 8 < 13 < 27. Take the small number i.e “ 2 “. Hence the left-most digit of the answer is 2. So our answer = 24

Solved Examples for Cube Root Formula

Example: Find Cube Root of 175616

Solution: Step 1- Take the last three digits and make their group i.e., 176 – 616

Step 2- Take the last digit of the above-formed group, i.e. 6. According to the cube rules table if the last digit having 6 then the last digit of cube root for that number is 6. Hence the last most digit of the cube root of the given number is 6

Step 3- Take the leftover group which is 176. We know that  176 lies in between the cube of the numbers i.e 5and 63. 125 < 176 < 216. Take the small cube number i.e “ 5 “. Hence the left-most digit of the answer is 5

So our answer = 56

So, using the above simple method we can calculate the cube root of a given number easily. This method can come handy while solving the questions.

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