To simplify \( 3\sqrt{343} \), we start by simplifying the square root.
First, we factor 343:
\[ 343 = 7^3 \]
Thus, we can rewrite \(\sqrt{343}\) as:
\[ \sqrt{343} = \sqrt{7^3} = \sqrt{7^2 \cdot 7} = \sqrt{7^2} \cdot \sqrt{7} = 7\sqrt{7} \]
Now, substituting this back into the original expression:
\[ 3\sqrt{343} = 3 \cdot 7\sqrt{7} = 21\sqrt{7} \]
So, the simplified form of \( 3\sqrt{343} \) is:
\[ \boxed{21\sqrt{7}} \]