Question

Which numbers are irrational? Select the three that apply.(3 points)
Responses

9–√
square root of 9

18−−√
square root of 18

169−−−√
square root of 169

78−−√
square root of 78

π
pi

9/15

Answer 1

To identify which numbers are irrational, we can analyze each option:

1. **\(\sqrt{9}\) (square root of 9)**: This equals 3, which is a rational number.
2. **\(\sqrt{18}\)**: This can be simplified to \(3\sqrt{2}\), and since \(\sqrt{2}\) is irrational, \(\sqrt{18}\) is also irrational.
3. **\(\sqrt{169}\) (square root of 169)**: This equals 13, which is a rational number.
4. **\(\sqrt{78}\)**: This does not simplify to an integer or a rational number; it involves \(\sqrt{39}\), which is also irrational. Thus, \(\sqrt{78}\) is irrational.
5. **\(\pi\)**: This is well-known to be an irrational number.
6. **\(\frac{9}{15}\)**: This simplifies to \(\frac{3}{5}\), which is a rational number.

From the analysis, the three irrational numbers are:

- \(\sqrt{18}\)
- \(\sqrt{78}\)
- \(\pi\)

So the selected responses are: **\(\sqrt{18}\), \(\sqrt{78}\), and \(\pi\)**.