To determine which of the following square roots results in a rational number, we need to evaluate the square roots of each given number and determine if they produce an integer result. A number is rational if it can be expressed as a ratio of two integers, which includes all integers and fractions.
Let's go through the numbers one by one:
1. [tex]\(\sqrt{2.56}\)[/tex]:
- Evaluating the square root of 2.56, we get approximately 1.6. Since 1.6 is not an integer, [tex]\(\sqrt{2.56}\)[/tex] is not rational.
2. [tex]\(\sqrt{10.0}\)[/tex]:
- Evaluating the square root of 10.0, we get approximately 3.162. Since 3.162 is not an integer, [tex]\(\sqrt{10.0}\)[/tex] is not rational.
3. [tex]\(\sqrt{28.9}\)[/tex]:
- Evaluating the square root of 28.9, we get approximately 5.376. Since 5.376 is not an integer, [tex]\(\sqrt{28.9}\)[/tex] is not rational.
4. [tex]\(\sqrt{32.4}\)[/tex]:
- Evaluating the square root of 32.4, we get approximately 5.7. Since 5.7 is not an integer, [tex]\(\sqrt{32.4}\)[/tex] is not rational.
None of the given square roots yield integer results, so none of them are rational. Therefore, the correct answer is that none of the given options represent a rational number.
