Question

Which numbers are irrational? Select the three that apply. (3 points)
square root of 78
square root of 169
square root of 18
pi
square root of 9

Answer 1

To identify which of the given numbers are irrational, let's analyze each option:

1. **Square root of 78 (\(\sqrt{78}\))**: This is an irrational number because 78 is not a perfect square.

2. **Square root of 169 (\(\sqrt{169}\))**: This is a rational number because it equals 13, which is an integer.

3. **Square root of 18 (\(\sqrt{18}\))**: This is an irrational number because 18 is not a perfect square. It simplifies to \(3\sqrt{2}\), which is still irrational.

4. **Pi (\(\pi\))**: This is an irrational number because it cannot be expressed as a fraction of two integers.

5. **Square root of 9 (\(\sqrt{9}\))**: This is a rational number because it equals 3, which is an integer.

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

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