Question

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

915
9 over 15

9–√
square root of 9

169−−−√
square root of 169

18−−√
square root of 18

π
pi

78−−√
square root of 78

Answer 1

To identify the irrational numbers from the options given, we need to determine which of these numbers cannot be expressed as a simple fraction (i.e., they are not exact fractions or integers). Here are the evaluations of each option:

1. **915**: This is an integer, so it is a rational number.

2. **9 over 15**: This simplifies to \( \frac{3}{5} \), which is a rational number.

3. **√9**: The square root of 9 equals 3, an integer, so it is rational.

4. **√169**: The square root of 169 equals 13, also an integer, making it rational.

5. **π (pi)**: Pi is a well-known irrational number that cannot be expressed as a simple fraction.

6. **√18**: The square root of 18 can be simplified to \( 3\sqrt{2} \), which is irrational because \( \sqrt{2} \) is irrational.

7. **√78**: The square root of 78 is also irrational since it cannot be simplified to a fraction.

From the analysis, the three irrational numbers are:

1. π (pi)
2. √18
3. √78

So, the correct selections for irrational numbers are π, √18, and √78.