To determine which product yields an irrational number, let's evaluate each option:
A. \( \sqrt{9} \times 3 \)
\[ \sqrt{9} = 3 \]
\[ 3 \times 3 = 9 \] (which is a rational number)
B. \( \frac{7}{8} \times \sqrt{25} \)
\[ \sqrt{25} = 5 \]
\[ \frac{7}{8} \times 5 = \frac{35}{8} \] (which is a rational number)
C. \( 2 \sqrt{64} \times 7 \sqrt{81} \)
\[ \sqrt{64} = 8 \quad \text{and} \quad \sqrt{81} = 9 \]
\[ 2 \times 8 \times 7 \times 9 = 2 \times 8 \times 63 = 1008 \] (which is a rational number)
D. \( 4 \sqrt{5} \times 2 \sqrt{49} \)
\[ \sqrt{49} = 7 \]
\[ 4 \sqrt{5} \times 2 \times 7 = 8 \sqrt{5} \] (which is an irrational number, since \( \sqrt{5} \) is irrational)
From the evaluations, option D yields an irrational number.
Thus, the answer is D. 4 sqrt5 times 2 sqrt49.