Question
Which numbers are rational? Check the%C2%A0three that apply.(3 points) Responses 72−−√ square root of 72 14−−√ square root of 14 π pi 1123 11 over 23 36−−√ square root of 36 2.7
Answers
GPT-4o mini
Rational numbers are numbers that can be expressed as a fraction of two integers, \( \frac{a}{b} \), where \( b \neq 0 \). Let's analyze the provided options:
1. **\( \sqrt{72} \)** - Not a rational number, since 72 is not a perfect square and cannot be expressed as a fraction of integers.
2. **\( \sqrt{14} \)** - Not a rational number, since 14 is not a perfect square and cannot be expressed as a fraction of integers.
3. **\( \pi \)** - Not a rational number, as pi is an irrational number.
4. **\( \frac{11}{23} \)** - This is a rational number because it is expressed as a fraction of two integers.
5. **\( \sqrt{36} \)** - A rational number, as \( \sqrt{36} = 6 \), which is an integer.
6. **\( 2.7 \)** - This is a rational number because it can be expressed as \( \frac{27}{10} \).
The three rational numbers from the list are \( \frac{11}{23} \), \( \sqrt{36} \), and \( 2.7 \).
1. **\( \sqrt{72} \)** - Not a rational number, since 72 is not a perfect square and cannot be expressed as a fraction of integers.
2. **\( \sqrt{14} \)** - Not a rational number, since 14 is not a perfect square and cannot be expressed as a fraction of integers.
3. **\( \pi \)** - Not a rational number, as pi is an irrational number.
4. **\( \frac{11}{23} \)** - This is a rational number because it is expressed as a fraction of two integers.
5. **\( \sqrt{36} \)** - A rational number, as \( \sqrt{36} = 6 \), which is an integer.
6. **\( 2.7 \)** - This is a rational number because it can be expressed as \( \frac{27}{10} \).
The three rational numbers from the list are \( \frac{11}{23} \), \( \sqrt{36} \), and \( 2.7 \).