Question

Which product yields an irrational number?
A. sqrt9 x 3
B. 7/8 x sqrt25
C. 2sqrt64 x 7sqrt81
D. 4sqrt5 x 2sqrt49

Answer 1

To determine which product yields an irrational number, let's evaluate each option step by step:

A. \( \sqrt{9} \times 3 \)
\[
\sqrt{9} = 3 \quad \Rightarrow \quad 3 \times 3 = 9
\]
(9 is a rational number)

B. \( \frac{7}{8} \times \sqrt{25} \)
\[
\sqrt{25} = 5 \quad \Rightarrow \quad \frac{7}{8} \times 5 = \frac{35}{8}
\]
(\(\frac{35}{8}\) is a rational number)

C. \( 2\sqrt{64} \times 7\sqrt{81} \)
\[
\sqrt{64} = 8 \quad \text{and} \quad \sqrt{81} = 9 \quad \Rightarrow \quad 2 \times 8 \times 7 \times 9 = 2 \times 8 \times 63 = 1008
\]
(1008 is a rational number)

D. \( 4\sqrt{5} \times 2\sqrt{49} \)
\[
\sqrt{49} = 7 \quad \Rightarrow \quad 4\sqrt{5} \times 2 \times 7 = 8\sqrt{5}
\]
(8\(\sqrt{5}\) is an irrational number, since \(\sqrt{5}\) is not a perfect square)

Based on this evaluation:

- A yields a rational number.
- B yields a rational number.
- C yields a rational number.
- D yields an irrational number.

Thus, the answer is:
**D. \( 4\sqrt{5} \times 2\sqrt{49} \)** yields an irrational number.