Which numbers are rational? Check the three that apply.(3 points) Responses 72−−√ square root of 72 2.7 2 point 7 1123 11 over 23 14−−√ square root of 14 π pi 36−−√

Answer 1

Rational numbers are numbers that can be expressed as the quotient of two integers (i.e., \( \frac{a}{b} \) where \( b \neq 0 \)). Let's check each of the numbers given:

1. \( \sqrt{72} \): This is an irrational number since it cannot be expressed as a fraction of two integers.

2. 2.7: This is a rational number because it can be expressed as \( \frac{27}{10} \).

3. \( \frac{11}{23} \): This is a rational number since it is already in the form of a fraction of two integers.

4. \( \sqrt{14} \): This is an irrational number as it cannot be expressed as a fraction of two integers.

5. \( \pi \): This is an irrational number.

6. \( \sqrt{36} \): This equals 6, which is a rational number since it can be expressed as \( \frac{6}{1} \).

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

• 2.7
• \( \frac{11}{23} \)
• \( \sqrt{36} \) (which is 6)

So, the rational numbers among the options are 2.7, \( \frac{11}{23} \), and \( \sqrt{36} \).