Alegebra 1 Chapter 6 assessment 1) Evaluate the expression \( \sqrt[3]{343} \) A. \( 7 \sqrt{3} \) B. \( \sqrt[3]{7} \) C.7. \( D .7^{3} \)

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**