how to find out cube root of fractions?
Answers
Answer:
To find the cube root of a given number, proceed as follows:
Step I. Express the given number as the product of primes.
Step II. Make groups in triplets of the same prime.
Step III. Find the product of primes, choosing one from each triplet.
Step IV. This product is the required cube root of the given number.
Note: If the group in triplets of the same prime factors cannot complete, then the exact cube root cannot be found.
Solved Examples of Cube Root using step by step with explanation
1. Evaluate the cube root: ∛216
Solution:
By prime factorization, we have
216 = 2 × 2 × 2 × 3 × 3 × 3
= (2 × 2 × 2) × (3 × 3 × 3)
Therefore, ∛216 = (2 × 3) = 6
2. Evaluate the cube root: ∛343
Solution:
By prime factorization, we have
343 = 7 × 7 × 7
= (7 × 7 × 7).
Therefore, ∛343 = 7
3. Evaluate the cube root: ∛2744
Solution:
By prime factorization, we have
2744 = 2 × 2 × 2 × 7 × 7 × 7
= (2 × 2 × 2) × (7 × 7 × 7).
Therefore, ∛2744 = (2 × 7) = 14