Question

Find ∛3375 by using prime factorization show the working

Answer 1

To find ∛3375, first perform prime factorization to get 3³ × 5³, then group the factors into triples that form cubes, simplify, and multiply to get the final answer of 15.

Step-by-step explanation:

To find ∛3375 by using prime factorization, first factor 3375 into a product of prime numbers:

• 3375 = 3 × 3 × 3 × 5 × 5 × 5

Now group the factors into triples that form a cube:

• (3 × 3 × 3) × (5 × 5 × 5)

Each triple can be written as a cube:

• 3³ × 5³

∛(3³ × 5³) can be simplified to 3 ∛(3³) × 5 ∛(5³), which simplifies further to:

• 3 × 5

Therefore, ∛3375 = 3 × 5 = 15.