Question
Alegebra 1 Chapter 6 assessment 1) Evaluate the expression \( \sqrt[3]{343} \) A. \( 7 \sqrt{3} \) B. \( \sqrt[3]{7} \) C.7. \( D .7^{3} \)
Ask by Adkins Clarke. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The cube root of 343 is 7.
Solution
To evaluate the expression \( \sqrt[3]{343} \), let's break it down step by step.
### Step 1: Understand the Cube Root
The cube root of a number \( x \) is a value that, when multiplied by itself three times, gives \( x \). In mathematical terms:
\[ \sqrt[3]{x} = y \quad \text{if and only if} \quad y^3 = x \]
### Step 2: Apply to \( \sqrt[3]{343} \)
We need to find a number \( y \) such that:
\[ y^3 = 343 \]
### Step 3: Find the Appropriate Value
Let's test \( y = 7 \):
\[ 7^3 = 7 \times 7 \times 7 = 343 \]
Since \( 7^3 = 343 \), it follows that:
\[ \sqrt[3]{343} = 7 \]
### Conclusion
The correct answer is:
**C. 7**
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To evaluate the expression \( \sqrt[3]{343} \), we can break it down! The number 343 can be rewritten as \( 7^3 \), making the cube root calculation a whole lot simpler. So, \( \sqrt[3]{7^3} = 7 \). Therefore, the correct answer is C. 7! Want to know a little more fun math trivia? The cube root not only helps with numbers but also has practical uses in architecture and design, where understanding volume is key! And if you ever find yourself puzzled with roots or exponents, remember to check if the number might be a perfect power—it saves so much calculation time!
