Question

Which product is rational?(1 point)
Responses

12⋅5.3420941...

12⋅π
12 times pi

8⋅25−−√
8 times square root of 25

10⋅8–√
10 times square root of 8

Answer 1

A rational number is any number that can be expressed as the quotient of two integers (a fraction). Let's analyze each of the options:

1. **12⋅5.3420941...** - This is a product of a rational number (12) and an irrational number (5.3420941... is non-repeating and non-terminating), resulting in an irrational number.

2. **12⋅π** - This is a product of a rational number (12) and an irrational number (π), resulting in an irrational number.

3. **8⋅√25** - The square root of 25 is 5 (which is a rational number). Thus, this is the product of two rational numbers (8 and 5), resulting in a rational number.

4. **10⋅√8** - The square root of 8 can be expressed as 2√2 (which is irrational). Thus, this is a product of a rational number (10) and an irrational number (2√2), resulting in an irrational number.

Based on this analysis, the only product that is rational is:

**8⋅√25**