To simplify the expression \( \sqrt{10} + 6\sqrt{40} \), we start by simplifying \( \sqrt{40} \):
\[ \sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10} \]
Now, substituting \( \sqrt{40} \) into the expression:
\[ \sqrt{10} + 6\sqrt{40} = \sqrt{10} + 6(2\sqrt{10}) = \sqrt{10} + 12\sqrt{10} \]
Now, we can combine the like terms:
\[ \sqrt{10} + 12\sqrt{10} = (1 + 12)\sqrt{10} = 13\sqrt{10} \]
Thus, the simplified expression is:
\[ \boxed{13\sqrt{10}} \]