Evaluate $$ \placeholder{}^3\sqrt{64m^3} $$

To evaluate the expression $ \sqrt[3]{64m^3} $, follow these steps:

1. **Factor the expression inside the cube root:**
   \[
   64m^3 = 64 \times m^3
   \]

2. **Calculate the cube root of each factor separately:**
   - $ \sqrt[3]{64} $: The cube root of 64 is 4 because $ 4^3 = 4 \times 4 \times 4 = 64 $.
   - $ \sqrt[3]{m^3} $: The cube root of $ m^3 $ is $ m $ because $ (m)^3 = m^3 $.

3. **Combine the results:**
   \[
   \sqrt[3]{64m^3} = 4m
   \]

Thus, the evaluated expression is $ \boxed{4m} $.

Would you like more details, or do you have any questions?

---

Here are five related questions to explore:

1. What is the cube root of $ 125m^6 $?
2. How would you evaluate $ \sqrt[4]{81n^4} $?
3. If $ m = 2 $, what is the value of \( \

Learn how to evaluate the cube root of 64m^3 with a detailed step-by-step solution. This problem covers cube roots, exponentiation, and algebraic simplification. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation