Which product yields an irrational number?

Question

A. sqrt9 times 3
B. 7/8 times sqrt25
C. 2 sqrt64 times 7 sqrt81
D. 4 sqrt5 times 2 sqrt49

Answer 1

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. $2\sqrt{64}\times 7\sqrt{81}$
$$\sqrt{64}=8\text{and}\sqrt{81}=9$$
$$2\times 8\times 7\times 9=2\times 8\times 63=1008$$ (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.