Question

Which numbers are rational? Check the three that apply.(3 points)
Responses

36−−√
square root of 36

72−−√
square root of 72

2.7
2 point 7

14−−√
square root of 14

π
pi

11/23

Answer 1

To determine which numbers are rational, we need to recall that a rational number is any number that can be expressed as the quotient of two integers (i.e., in the form \( \frac{a}{b} \) where \( a \) and \( b \) are integers and \( b \neq 0 \)).

Now, let's evaluate each option:

1. **\( \sqrt{36} \)**:
- This equals 6, which is a whole number. Hence, it is rational.

2. **\( \sqrt{72} \)**:
- This equals \( 6\sqrt{2} \), which is an irrational number (since \( \sqrt{2} \) is irrational). So, this is not rational.

3. **2.7**:
- This can be expressed as \( \frac{27}{10} \), which is a fraction of two integers. Therefore, it is rational.

4. **\( \sqrt{14} \)**:
- This is an irrational number. So, this is not rational.

5. **\( \pi \)**:
- This is a well-known irrational number. So, this is not rational.

6. **\( \frac{11}{23} \)**:
- This is already in the form of a fraction where both 11 and 23 are integers, with 23 not equal to zero. Therefore, it is rational.

**In summary, the three rational numbers from the list are:**
- \( \sqrt{36} \)
- 2.7
- \( \frac{11}{23} \)