The question asks for the cube root of 343 ($\sqrt[3]{343}$).

The cube root of a number is a value that, when multiplied by itself three times, equals the original number.

To calculate: $\sqrt[3]{343} = x \quad \text{where} \quad x^3 = 343$

Since $7 \times 7 \times 7 = 343$, we find: $\sqrt[3]{343} = 7$

Answer: 7

Would you like a detailed explanation of cube roots or additional practice problems?

Here are 5 related questions for exploration:

1. What is the cube root of 729?
2. How do you find the cube root of a decimal like 0.125?
3. What are the steps to estimate cube roots of non-perfect cubes?
4. Can a negative number have a real cube root? If so, find $\sqrt[3]{-27}$.
5. How do cube roots relate to powers in mathematics?

Tip: The cube root of a perfect cube is always an integer!