Question

Which of the following numbers are rational? (Select all that apply.)

A.
√64

B.
0.145874…

C.
0.75

D.
-8

Answer 1

To determine which numbers are rational, we need to identify if they can be expressed as a fraction of two integers (where the denominator is not zero).

A. **√64**
- The square root of 64 is 8, which can be expressed as 8/1. Therefore, it is rational.

B. **0.145874…**
- This number is a non-terminating and repeating decimal. Although it appears to be non-terminating, if it was repeating, it could be considered rational. However, without more information, on its own it is not established as repeating (though we should assume for the sake of this, it is a decimal to some further extent). Let's tentatively classify it as not rational until proven.

C. **0.75**
- This number can be expressed as 75/100, which simplifies to 3/4. Therefore, it is rational.

D. **-8**
- This number can be expressed as -8/1. Therefore, it is rational.

In conclusion, the rational numbers from the list are:

- A. √64
- C. 0.75
- D. -8

**So, A, C, and D are rational.** B may not be rational unless proven otherwise as a repeating decimal.