The expression you have provided is the cube root of 343, denoted as $\sqrt[3]{343}$.

To solve for the cube root of 343, we first look for a number which, when cubed, equals 343.

We know that: $7^3 = 7 \times 7 \times 7 = 343$

Thus, the cube root of 343 is: $\sqrt[3]{343} = 7$

Would you like more details or have any questions?

Here are some related questions:

1. What is the cube root of other perfect cubes like 64 or 512?
2. How do you calculate cube roots of numbers that are not perfect cubes?
3. What is the difference between square roots and cube roots?
4. How do you simplify expressions with higher roots, such as the fourth or fifth roots?
5. How can cube roots be applied in real-world scenarios?

Tip: When dealing with cube roots, identifying perfect cubes can make calculations much faster.