Question

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

2.7
2 point 7

14−−√
square root of 14

36−−√
square root of 36

π
pi

72−−√
square root of 72

1123

Answer 1

Rational numbers are numbers that can be expressed as the quotient or fraction of two integers (where the denominator is not zero).

Let's analyze the provided options:

1. **2.7** - This is a decimal that can be expressed as the fraction \( \frac{27}{10} \), so it is a rational number.

2. **\( \sqrt{14} \)** - This cannot be expressed as a fraction of two integers and is an irrational number.

3. **\( \sqrt{36} \)** - This equals 6, which is a whole number and can be expressed as \( \frac{6}{1} \), so it is a rational number.

4. **\( \pi \)** - This is a well-known irrational number, so it is not rational.

5. **\( \sqrt{72} \)** - This can be simplified to \( 6\sqrt{2} \), which is also not expressible as a fraction of two integers and is thus irrational.

6. **1123** - This is a whole number and can be expressed as \( \frac{1123}{1} \), so it is a rational number.

Based on the analysis, the three numbers that are rational are:

- 2.7
- \( \sqrt{36} \)
- 1123