Question

Which numbers are rational? Check the three that apply.(3 points)
Responses

70−−√
square root of 70

32−−√
square root of 32

4.52525252...

π
pi

1217
12 over 17

16−−√

Answer 1

To determine which numbers are rational, we need to identify numbers that can be expressed as the quotient of two integers (i.e., in the form a/b, where a and b are integers and b is not zero).

1. **\( \sqrt{70} \)**: This is an irrational number because 70 is not a perfect square.

2. **\( \sqrt{32} \)**: This is also irrational because it can be simplified to \( \sqrt{16} \cdot \sqrt{2} = 4\sqrt{2} \), and \(\sqrt{2}\) is irrational.

3. **4.52525252...**: This is a repeating decimal, which is rational. It can be expressed as a fraction.

4. **π (pi)**: This is known to be an irrational number.

5. **1217**: This is an integer and therefore rational (it can be expressed as \( 1217/1 \)).

6. **\( \sqrt{16} \)**: This is equal to 4, which is a rational number.

Based on this analysis, the rational numbers from the choices provided are:

- **4.52525252...**
- **1217**
- **\( \sqrt{16} \)**

So, the three rational numbers are:

- 4.52525252...
- 1217
- \( \sqrt{16} \)