Question

Which numbers are irrational? Check the three that apply.

- \sqrt(12)
- 1.7
- \sqrt(80)
- 7/18
- \sqrt(16)
- pi

Answer 1

To determine which of the given numbers are irrational, let's analyze each one:

1. **\(\sqrt{12}\)**: This can be simplified to \(2\sqrt{3}\). Since \(\sqrt{3}\) is irrational, \(\sqrt{12}\) is also irrational.

2. **1.7**: This is a decimal number and can be expressed as the fraction \(\frac{17}{10}\), which is a rational number.

3. **\(\sqrt{80}\)**: This can be simplified to \(4\sqrt{5}\). Since \(\sqrt{5}\) is irrational, \(\sqrt{80}\) is also irrational.

4. **\(\frac{7}{18}\)**: This is a fraction and is thus a rational number.

5. **\(\sqrt{16}\)**: This equals 4, which is a rational number.

6. **\(\pi\)**: This is a well-known irrational number; it cannot be expressed as a fraction of two integers.

Based on the analysis, the three irrational numbers from the list are:

- \(\sqrt{12}\)
- \(\sqrt{80}\)
- \(\pi\)

So the final answer is:

- **\(\sqrt{12}\)**
- **\(\sqrt{80}\)**
- **\(\pi\)**