To determine which product yields an irrational number, we need to evaluate each option.
A. \( \sqrt{9} \cdot 3 = 3 \cdot 3 = 9 \) (rational)
B. \( \frac{7}{8} \cdot \sqrt{25} = \frac{7}{8} \cdot 5 = \frac{35}{8} \) (rational)
C. \( 2\sqrt{64} \cdot 7\sqrt{81} = 2 \cdot 8 \cdot 7 \cdot 9 = 2 \cdot 7 \cdot 72 = 1008 \) (rational)
D. \( 4\sqrt{5} \cdot 2\sqrt{49} = 4\sqrt{5} \cdot 2 \cdot 7 = 8\sqrt{5} \cdot 7 = 56\sqrt{5} \) (irrational, because \( \sqrt{5} \) is irrational)
The product that yields an irrational number is:
D. \( 4\sqrt{5} \cdot 2\sqrt{49} \).
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