Question

Which numbers are irrational? Check the three that apply.





(3 points)
Responses

7/18
7 over 18

π
pi

16−−√
square root of 16

12−−√
square root of 12

1.7
1 point 7

80−−√

Answer 1

To identify which numbers are irrational, we should recall that irrational numbers cannot be expressed as a fraction of two integers (i.e., they cannot be represented as p/q, where p and q are integers and q is not zero). Common examples of irrational numbers include non-repeating and non-terminating decimals, and certain square roots.

Let's analyze each option:

1. **7/18**: This is a fraction and can be expressed as a ratio of two integers, so it is a rational number.

2. **π**: Pi is a well-known irrational number, as it cannot be expressed as a fraction.

3. **√16**: The square root of 16 equals 4, which is a whole number (and thus rational).

4. **√12**: The square root of 12 simplifies to 2√3, which is not a perfect square and cannot be expressed as a fraction of two integers, making it an irrational number.

5. **1.7**: This is a terminating decimal and can be expressed as the fraction 17/10, so it is a rational number.

6. **√80**: The square root of 80 simplifies to 4√5, which is not a perfect square and cannot be expressed as a fraction of two integers, making it an irrational number.

Based on this analysis, the three irrational numbers are:

- π
- √12
- √80