Question

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

π
pi

70−−√
square root of 70

32−−√
square root of 32

1217
12 over 17

4.52525252...

16−−√

Answer 1

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

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

2. **√70 (square root of 70)** - This is also an irrational number, as 70 is not a perfect square and cannot be expressed as a fraction of two integers.

3. **√32 (square root of 32)** - This can be simplified to \(4\sqrt{2}\), which is also irrational (since \(\sqrt{2}\) is irrational).

4. **1217 (12 over 17)** - This is a rational number because it is expressed as a fraction of two integers.

5. **4.52525252...** - This is a rational number, as it has a repeating decimal (represented as \(4.5\overline{25}\)), which can be expressed as a fraction.

6. **√16** - This is equal to 4, which is a rational number because it can be expressed as \(\frac{4}{1}\).

Based on this assessment, the three rational numbers from the options are:

- **1217 (12 over 17)**
- **4.52525252...**
- **√16**

Therefore, your selection should include these three options.