How to Find Cube Root

Here, we will learn how to find cube root of a number, by prime factorization method. It is not an easy task to find the cube root but a complex process. To find the cube root of a number, we need to find a number which when multiplied three times by itself gives the original number.

Example: ∛8 = ∛(2 × 2 × 2) = 2

We will study how we can calculate the cube root of any given number in this article. We will also study the importance of knowing the cube of the numbers as in finding the cube root. Let’s list out the important topics covered in this article:

  • Finding the cube root
  • Cube Root Table
  • Cube roots of numbers 1 to 15
  • Finding the cube root by prime factorisation method

Finding the cube root

Cube root is the inverse process of calculating the cube of a number. The symbol  denotes the cube root. Also, find cube root formula here, which will give you the original number, whose cube is given to us. For example,

To find the cube root of a number 64, we want a number which when multiplied thrice with itself shall give 64. We can write,

64 = 4 × 4× 4 = 43

Taking cubic root on both the sides;

or 64 = 43

Therefore, cube-root of 64 is 4.

Please note that we will only consider the positive values cube roots of the natural numbers.

Cube Root Table

Number Cube Cube root
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

Cubes from 1 to 15

Cube root

Cube

3√1 = 1

1

3√8 =2

8

3√27 = 3

27

3√64 = 4

64

3√125 = 5

125

3√216 = 6

216

3√343 = 7

343

3√512 = 8

512

3√729 = 9

729

3√1000 = 10

1000

3√1331 = 11

1331

3√1728 = 12

1728

3√2197 =13

2197

3√2744 = 14

2744

3√3375 = 15

3375

Prime Factorisation Method

We can find the cube-root of a number by the method of prime factorisation. Consider the following example for a clear understanding:

2744= 2 × 2× 2 × 7 ×7 × 7= (2 ×7 )3

Therefore the cube root of 2744 = ∛2744 = 2 × 7 = 14

Illustration 1: Solve: 24389
Solution: Prime factors = 29×29×29 = 293
Therefore ∛24389= 29

Illustration 2: Find 46656 by the method of prime factorization.

Solution: Let us first find the prime factors:

Cube Root by Prime Factorisation Method

∛46656 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3 = 23 × 23 × 33 × 33 = (2 × 2 × 3 × 3)3

Therefore, 46656= 36

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Practise This Question

The value of  33375×115 is