To simplify \( 13\sqrt{27} \), we start by simplifying \( \sqrt{27} \).
We can break down \( 27 \) as follows:
\[ 27 = 9 \times 3 \]
Thus, we can rewrite the square root:
\[ \sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} \]
Since \( \sqrt{9} = 3 \), we have:
\[ \sqrt{27} = 3\sqrt{3} \]
Now we can substitute this back into the original expression:
\[ 13\sqrt{27} = 13 \times 3\sqrt{3} = 39\sqrt{3} \]
Therefore, the simplified form of \( 13\sqrt{27} \) is:
\[ \boxed{39\sqrt{3}} \]