Cube root using factorization method[With each step image]

In this post, you’ll learn the step-by-step process to find cube root using the prime factorization method. For that, we’ll first discuss the procedure of the prime factorization method for cube root. Then, see some solve examples and at the end, you’ll get practice problems with answers. So, you can check your concept with the help of these problems.

Let’s take an example and try to find its cube root using prime factorization.

Assumed number: 4096 

Procedure : 

Step: 01 Find the prime factor of the number using the factorization method 

Cube root of 4096

Step:02 Make triplets(Groups of three numbers) of the equal prime factors 

cube root procedure

 

Step:03 Write one prime factor instead of triplets obtained in step 2 to find cube root. 

Square root of 4096 using prime factorization method

Step: 04 Multiply prime factors obtained in step 3 . Result of this product is the cube root of the number

Thus,  2 × 2× 2×2 = 16 which is the cube root of 4096  

Example:01 

Find the cube root of 42875 using the prime factorization method 

Solution : 

Step: 1 Find the prime factor of 42875 

Prime factor of 42875 Step: 2 Make triplet of the obtained prime factor 

Cube root procedure

 

Step: 3 Write one prime factor instead of triplets.

Cube root of 42875

Step:04 Multiply obtained prime factor in step 3 i.e 5 and 7

Thus , the cube root of 42875 is 35 

Example:02

Find the cube root of 13824 using the prime factorization method

Solution: 

Step:01. Find the prime factor of 13824 using the factorization method

Cube root of 13824

Step:02 Make triplet of the obtained prime factor 

Step:03 Write one prime factor instead of triplets.

Cube root of 13824

Step:04 Multiply obtained prime factors i.e 2, 2,2,3 

Thus , Cube root of 13824 is 2×2×2×3=24 

I hope, you have understood the complete procedure to find cube root using the prime factorization method. Now it’s time to practice some problems yourself.

Practice these problems ……

Practice problems : 

Q.1 Find the cube root of the following numbers using the prime factorization method 

(i) 9261 

(ii) 6859 

(iii) 3375

(iv) 343 

(v) 5832000

(vi) 110592 

(vii) 592704 

(viii) 13824 

(ix) 2744 

Check answer:

(i) 21

(ii) 19 

(iii) 15

(iv) 7

(v) 180

(vi) 48

(vii) 84

(viii) 24

(ix) 14

Check these stuff as well 

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