Rewrite cube root of, 128, end cube root 
3
  
128
​
  in simplest form.

To rewrite \(\sqrt[3]{128}\) (the cube root of 128) in its simplest form, follow these steps:

1. **Prime Factorization of 128**:
   \[
   128 = 2^7
   \]

2. **Cube Roots**:
   We look for groups of three identical factors, as that's what a cube root simplifies:
   \[
   \sqrt[3]{2^7} = \sqrt[3]{2^6 \times 2} = 2^2 \times \sqrt[3]{2} = 4\sqrt[3]{2}
   \]

So, \(\sqrt[3]{128} = 4\sqrt[3]{2}\).

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the cube root of 64?
2. How do you simplify cube roots involving prime numbers?
3. What is the cube root of 343?
4. How do you handle cube roots for non-perfect cubes?
5. How is cube root simplification different from square root simplification?

**Tip**: Always factor numbers fully to spot cubes or squares when simplifying roots.

Rewrite cube root of 128 in simplest form.

Learn how to simplify the cube root of 128 using prime factorization. This detailed guide walks you through the cube root simplification process, suitable for students in Grades 7-10. Discover how 128 breaks down into prime factors and how to apply cube root properties for a simplified answer.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation