To determine whether the product of \(\sqrt{49}\) and \(1313\) is rational or irrational, we first evaluate \(\sqrt{49}\).
\[ \sqrt{49} = 7 \]
Next, we consider the number \(1313\), which is a whole number. Now we compute the product of \(7\) and \(1313\):
\[ 7 \times 1313 \]
Since both \(7\) (a rational number) and \(1313\) (also a rational number) are rational, their product will also be rational.
Thus, the product \(\sqrt{49} \times 1313\) is rational.