Introduction to 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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