1. Cube root – Prime Factorization

2. Cube Root - Prime Factorization Method
To find the cube root using the prime factorization method
Step I:  Factorize into prime factors.
Step II:  Make a group of 3 factors.
Step III:  Take out one factor from each group.

3. 1. Find the Cube root of 512 by prime factorization method. Solution:
Step 1: Factorize into prime factors, we get
Step 2: Make a group of 3 factors. 
Step 3: Take out one factors from each pair
512 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
512 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
∛512 = x x = 8
Therefore, ∛512 = 8

4. 2. Find the Cube root of 4096 by prime factorization method. Solution:
Step 1: Factorize into prime factors, we get
Step 2: Make a group of 3 factors. 
Step 3: Take out one factors from each pair
4096 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
4096 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
∛ 4096 = x x x
∛ = 16
Therefore, ∛ 4096 = 16

5. Try these
Evaluate
Evaluate 5832