Question

Which expression will equal a rational product even though it is multiplying an irrational number times another irrational number?

StartRoot 11 EndRoot times StartRoot 11 EndRoot
4.7813265 ellipsis times StartRoot 5 EndRoot
Pi times 3.785492 ellipsis
StartRoot 21 EndRoot times pi

Answer 1

To determine which expression results in a rational product while multiplying an irrational number by another irrational number, let's analyze each option:

1. \( \sqrt{11} \times \sqrt{11} \):
- This simplifies to \( 11 \), which is a rational number.

2. \( 4.7813265 \ldots \times \sqrt{5} \):
- Here, \( 4.7813265 \ldots \) is a decimal representation (likely irrational), and \( \sqrt{5} \) is also irrational. The product of two irrationals is not guaranteed to be rational.

3. \( \pi \times 3.785492 \ldots \):
- Here, \( \pi \) is irrational and \( 3.785492 \ldots \) appears to be irrational. Their product is also not guaranteed to be rational.

4. \( \sqrt{21} \times \pi \):
- Both \( \sqrt{21} \) and \( \pi \) are irrational numbers, and their product would also be irrational.

Based on this analysis, the only expression that equals a rational product (which is 11) is:

**\( \sqrt{11} \times \sqrt{11} \)**.