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CUBE ROOT (PRIME FACTORIZATION)

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Introduction to Cube root

cube_root_fac_1In Math, there is always an "opposite" operation! The opposite operation for "cubing" a number is taking the "cube root".


Cube root is the opposite of cubing a number.


Term for raising a number to the 3rd power is "cubing a number".



For example:

23 = 8 this can be read as 2 "cubed" equals 8.

This means that 2 x 2 x 2 = 8.


We represent cube root using this symbol ‘ ’


And to show that cube root is opposite of cubing a number, let have a look at the following example:

23 = 8 and  8 =  2 x 2 x 2 = 2



Finding Cube Root by Prime Factorization   

To find the cube root of a number by prime factorization, we follow the following steps:

Step I:
Find the prime factors of the given number.


Step II:
Make groups of 3 same factors.


Step III:
Take one prime factor from each group of prime factors of the given number.


Step IV:
Find the product of these prime factors to get the cube root of the given number.


Let’s understand this with example:


Find the cube root of 3375 by prime factorization.

Step I: Find the prime factors of the given number.
3375 = 3 x 3 x 3 x 5 x 5 x 5

Step II: Make groups of 3 same factors.

(3 x 3 x 3)
(5 x 5 x 5)

Step III: Take one prime factor from each group of prime factors of the given number.

(3 x 3 x 3) – 3
(5 x 5 x 5) – 5

Step IV: Find the product of these prime factors to get the cube root of the given number.

3 x 5 = 15

Hence the cube root of 3375 is 15.


Let’s try more examples to understand the concept better:


Find cube root of 5832 by prime factorization.

Step I: Find the prime factors of 5832
5832 = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3

Step II: Make groups of three same factors

2 x 2 x 2
3 x 3 x 3
3 x 3 x 3

Step III: Take one prime factor from each group of prime factors of 5832

2 x 2 x 2 - 2
3 x 3 x 3 - 3
3 x 3 x 3 – 3

Step IV: Find the product of these prime factors to get the cube root of the given number.

2 x 3 x 3 = 18

So, Cube root of 5832 is 18.



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