Question
Question 6 simplify the following radical expression. \( \sqrt[3]{64 x^{3}} \) O \( 4 x^{3} \) \( 04 x \) \( 08 x^{3} \) 8x
Ask by Sandoval Mccoy. in the United States
Jan 26,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified form of \( \sqrt[3]{64 x^{3}} \) is \( 4x \).
Solution
To simplify the radical expression \( \sqrt[3]{64 x^{3}} \), follow these steps:
1. **Break Down the Expression:**
\[
\sqrt[3]{64 x^{3}} = \sqrt[3]{64} \times \sqrt[3]{x^{3}}
\]
2. **Simplify Each Part Separately:**
- \( \sqrt[3]{64} = 4 \) because \( 4^3 = 64 \).
- \( \sqrt[3]{x^{3}} = x \) because the cube root and the exponent cancel each other out.
3. **Combine the Simplified Parts:**
\[
\sqrt[3]{64 x^{3}} = 4 \times x = 4x
\]
**Final Answer:** \( 4x \)
Among the provided options, the correct simplified form is **4x**.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To simplify the radical expression \( \sqrt[3]{64 x^{3}} \), you can break it down as follows: First, recognize that \( 64 \) can be expressed as \( 4^3 \). Therefore, \( \sqrt[3]{64} = 4 \). Next, since \( x^3 \) is also a perfect cube, \( \sqrt[3]{x^3} = x \). By combining these results, we get \( \sqrt[3]{64 x^3} = 4x \). So, the correct answer is \( 4x \). But remember, always check to see if the expression is in simplest form! When simplifying radical expressions, ensure you didn’t miss any common bases or leftover roots. It can be easy to overlook factors, so take a moment to verify your steps to avoid mistakes!
