To simplify $\sqrt{343}$, let's start by factoring 343.

First, observe that:

$343 = 7^3$

Therefore,

$\sqrt{343} = \sqrt{7^3}$

We can simplify this expression using the property of square roots:

$\sqrt{7^3} = \sqrt{7^2 \cdot 7} = 7 \cdot \sqrt{7}$

So, the simplified form of $\sqrt{343}$ is:

$7\sqrt{7}$

Would you like more details or help with something else? Here's a list of related questions:

1. How do you simplify square roots of other cube numbers?
2. What other numbers can be expressed as powers of 7?
3. How do you approximate the value of $\sqrt{343}$?
4. Can you simplify other square roots with exponents greater than 2?
5. What are the properties of square roots involving prime numbers?

Tip: When simplifying square roots, look for perfect squares or powers that can be factored out.