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

Question

Responses
32−−√
square root of 32
π
pi
4.52525252...
70−−√
square root of 70
12/17
12 over 17
16−−√

Answer 1

To determine which numbers are rational, we need to understand the definition of rational numbers. A rational number is any number that can be expressed as a fraction \( \frac{a}{b} \) where \( a \) and \( b \) are integers, and \( b \) is not zero.

Let's evaluate the provided options:

1. \( \sqrt{32} \) - This number is an irrational number because it cannot be expressed as a fraction of two integers.

2. \( \pi \) - This is also an irrational number and cannot be expressed as a simple fraction.

3. \( 4.52525252... \) - This number has a repeating decimal (the "52" repeats), which can be expressed as a fraction. Therefore, it is a rational number.

4. \( \sqrt{70} \) - Similar to \( \sqrt{32} \), \( \sqrt{70} \) is an irrational number.

5. \( \frac{12}{17} \) - This is a fraction of two integers and is therefore a rational number.

6. \( \sqrt{16} \) - This evaluates to 4, which is a whole number and can be expressed as \( \frac{4}{1} \), thus it is a rational number.

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

• \( 4.52525252... \)
• \( \frac{12}{17} \)
• \( \sqrt{16} \)

So the final selected rational numbers are:

1. \( 4.52525252... \)
2. \( \frac{12}{17} \)
3. \( \sqrt{16} \)