Question

Which numbers are rational? Check the three that apply.(3 points) Responses π pi 16−−√ square root of 16 70−−√ square root of 70 1217 12 over 17 4.52525252... 32−−√ square root of 32

Answer 1

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

1. **π (pi)** - This is an irrational number. It cannot be expressed as a fraction of two integers.

2. **√16 (square root of 16)** - This is a rational number. √16 = 4, which can be expressed as 4/1.

3. **√70 (square root of 70)** - This is an irrational number because it cannot be expressed as a fraction of integers.

4. **1217 (12 over 17)** - This is a rational number. It can be expressed as 12/17.

5. **4.52525252...** - This is a rational number because it is a repeating decimal. It can be expressed as a fraction (specifically \( \frac{181}{40} \) when simplified).

6. **√32 (square root of 32)** - This is also an irrational number because it cannot be expressed as a fraction of two integers.

Based on this analysis, the three numbers that are rational are:

- √16
- 1217
- 4.52525252...

So your selections should be **√16, 1217, and 4.52525252...**.