Question

Which product yields an irrational number?
A. square root of 9 * 3

B. 7/8 * square root of 25

C. 2\sqrt(64)*7\sqrt(81)

D. 4\sqrt(5)*2\sqrt(49)

Answer 1

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

A. \( \sqrt{9} \times 3 \)
- \( \sqrt{9} = 3 \)
- So, \( 3 \times 3 = 9 \) (which is rational).

B. \( \frac{7}{8} \times \sqrt{25} \)
- \( \sqrt{25} = 5 \)
- So, \( \frac{7}{8} \times 5 = \frac{35}{8} \) (which is rational).

C. \( 2\sqrt{64} \times 7\sqrt{81} \)
- \( \sqrt{64} = 8 \) and \( \sqrt{81} = 9 \)
- So, \( 2 \times 8 \times 7 \times 9 = 2 \times 56 \times 9 = 1008 \) (which is rational).

D. \( 4\sqrt{5} \times 2\sqrt{49} \)
- \( \sqrt{49} = 7 \)
- So, \( 4\sqrt{5} \times 2 \times 7 = 8\sqrt{5} \) (which is irrational since \( \sqrt{5} \) is irrational).

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