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...

1 answer

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