Question

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

9–√
square root of 9

915
9 over 15

78−−√
square root of 78

18−−√
square root of 18

π
pi

169−−−√

Answer 1

To identify which numbers are irrational from the list, let's evaluate each one:

1. **9 - √ (square root of 9)**:
- The square root of 9 is 3, which is a rational number. Therefore, this is not irrational.

2. **915 (9 over 15)**:
- 9/15 simplifies to 3/5, which is also a rational number. Thus, this is not irrational.

3. **78 −−√ (square root of 78)**:
- The square root of 78 cannot be expressed as a fraction of two integers, as it has a non-repeating, non-terminating decimal. Therefore, this is an irrational number.

4. **18 −−√ (square root of 18)**:
- The square root of 18 simplifies to 3√2. Since √2 is irrational, 3√2 is also irrational. Thus, this is an irrational number as well.

5. **π (pi)**:
- Pi is a well-known irrational number. It cannot be expressed as a fraction of two integers. Therefore, this is also irrational.

6. **169 −−−√ (square root of 169)**:
- The square root of 169 is 13, which is a rational number. Therefore, this is not irrational.

The three irrational numbers from the options given are:

1. **√78**
2. **√18**
3. **π**