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Home >> Cube Root >> Cube Root by Prime Factorization Method >> Cube Root by Prime Factorization Method
Before you study How to calculate Cube Root by Prime Factorization Method, you are adviced to read:
What are Cube Numbers ?
What is a Cube Root ?
What is Prime Factorization ?
Steps of finding Cube root by prime factorization method:
Step 1: Find Prime Factorization of given number
Step 2: Make one group of three same prime factors
Step 3: Collect one prime factor from each group
Step 4: Multiply the collected prime factors ( if only one pair, ignore this step)
Step 5: Resultant number is the cube root of the given number
Example 1: Find cube root of 8 using prime factorization method.
Solution: Steps are as follows:
Step 1: Find Prime Factorization of given number and we get:
Prime Factorization of 8 = 2 X 2 X 2
Step 2: Make one group of three same prime factors and we get:
= 2 X 2 X 2
Step 3: Collect one prime factor from each group
= 2
Step 5: Resultant number is the cube root of the given number and we get:
2 is the cube root of 8
Or we can write it as:
∛ 8 = 2
Example 2: Find cube root of 216 using prime factorization method.
Solution: Steps are as follows:
Step 1: Find Prime Factorization of given number and we get:
Prime Factorization of 216 = 2 X 2 X 2 X 3 X 3 X 3
Step 2: Make one group of three same prime factors and we get:
= 2 X 2 X 2 X 3 X 3 X 3
Step 3: Collect one prime factor from each group
= 2 X 3
Step 4: Multiply the collected prime factors and we get:
= 6
Step 5: Resultant number is the cube root of the given number
6 is the cube root of 216
Or we can write it as:
∛ 216 = 6
Example 3: Find cube root of 1000 using prime factorization method.
Solution: Steps are as follows:
Step 1: Find Prime Factorization of given number and we get:
Prime Factorization of 1000 = 2 X 2 X 2 X 5 X 5 X 5
Step 2: Make one group of three same prime factors and we get:
= 2 X 2 X 2 X 5 X 5 X 5
Step 3: Collect one prime factor from each group
= 2 X 5
Step 4: Multiply the collected prime factors and we get:
= 10
Step 5: Resultant number is the cube root of the given number
10 is the cube root of 1000
Or we can write it as:
∛ 1000 = 10
Example 4: Find cube root of 74088 using prime factorization method.
Solution: Steps are as follows:
Step 1: Find Prime Factorization of given number and we get:
Prime Factorization of 74088 = 2 X 2 X 2 X 3 X 3 X 3 X 7 X 7 X 7
Step 2: Make one group of three same prime factors and we get:
= 2 X 2 X 2 X 3 X 3 X 3 X 7 X 7 X 7
Step 3: Collect one prime factor from each group
= 2 X 3 X 7
Step 4: Multiply the collected prime factors and we get:
= 42
Step 5: Resultant number is the cube root of the given number
42 is the cube root of 74088
Or we can write it as:
∛ 74088 = 42
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