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

Question

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
• \( \frac{11}{23} \)