Which product is rational?(1 point) Responses 12⋅π12⋅π12 times pi 8⋅25−−√8⋅258 times square root of 25 12⋅5.3420941...12⋅5.3420941... 10⋅8–√

Answer 1

To determine which of the given products is rational, we need to evaluate each option:

1. \( 12 \cdot \pi \):

   • \(\pi\) is an irrational number. Therefore, \(12 \cdot \pi\) is also irrational.

2. \( 8 \cdot \sqrt{25} \):

   • \(\sqrt{25} = 5\), which is a rational number, so \(8 \cdot 5 = 40\) is rational.

3. \( 12 \cdot 5.3420941... \):

   • The number \(5.3420941...\) appears to be a non-terminating decimal, which suggests it is irrational. Hence, \(12 \cdot 5.3420941...\) is likely irrational.

4. \( 10 \cdot \sqrt{8} \):

   • \(\sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2}\). Since \(\sqrt{2}\) is irrational, \(10 \cdot 2\sqrt{2} = 20\sqrt{2}\) is also irrational.

Thus, the only rational product is:

\( 8 \cdot \sqrt{25} = 40 \).