Question

Which numbers are rational? Check the three that apply.(3 points)Responses16−−√square root of 1632−−√square root of 3270−−√square root of 70πpi121712 over 174.52525252..

Answer 1

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

Let’s check the given responses:

1. **\(16−−√\) (square root of 16)**:
- \(\sqrt{16} = 4\), which is a whole number. This is a rational number.

2. **\(32−−√\) (square root of 32)**:
- \(\sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2}\). Since \(\sqrt{2}\) is an irrational number, \(4\sqrt{2}\) is also irrational. This is not a rational number.

3. **\(70−−√\) (square root of 70)**:
- \(\sqrt{70}\) cannot be expressed as a fraction of two integers, so it is irrational. This is not a rational number.

4. **\(\pi\)**:
- \(\pi\) is known to be an irrational number. This is not a rational number.

5. **\(121712 \over 174\)**:
- This is a fraction representing the division of two integers (121712 and 174), so it is a rational number.

6. **\(52525252.. \)** (recurring decimal):
- The notation \(0.52525252...\) (which denotes \(0.52\) repeating) is a rational number because it can be expressed as a fraction.

Based on the analysis, the rational numbers among the options are:

1. \( \sqrt{16} \) (4)
2. \( \frac{121712}{174} \)
3. \( 0.52525252... \) (the repeating decimal)

So the correct responses are:
- \( \sqrt{16} \)
- \( \frac{121712}{174} \)
- \( 0.52525252... \)