Question

Which product is rational?(1 point)
Responses

8⋅25−−√
8 times square root of 25

10⋅8–√
10 times square root of 8

12⋅π
12 times pi

12⋅5.3420941...

Answer 1

To determine which product is rational, we need to analyze each option:

1. **\(8 \cdot \sqrt{25}\)**:
- The square root of 25 is 5, so this simplifies to \(8 \cdot 5 = 40\), which is a rational number.

2. **\(10 \cdot \sqrt{8}\)**:
- The square root of 8 is \(\sqrt{4 \cdot 2} = 2\sqrt{2}\), making it \(10 \cdot 2\sqrt{2} = 20\sqrt{2}\). Since \(\sqrt{2}\) is irrational, this product is irrational.

3. **\(12 \cdot \pi\)**:
- Since \(\pi\) is an irrational number, this product (\(12 \pi\)) is also irrational.

4. **\(12 \cdot 5.3420941...\)**:
- The number \(5.3420941...\) seems to be a decimal representation of a rational number, but we don't know if it terminates or is a repeating decimal. However, if it's just a non-terminating decimal with no specific repeating pattern indicated, we can't assume it's rational based on the number given.

The only option which we can confidently say is rational is:

- **\(8 \cdot \sqrt{25}\)**, which equals 40.

Thus, the rational product is \(8 \cdot \sqrt{25}\).