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

Question

Responses

72−−√
square root of 72

11/23
11 over 23

14−−√
square root of 14

36−−√
square root of 36

2.7
2 point 7

π

Answer 1

Rational numbers are numbers that can be expressed as the quotient of two integers (i.e., a fraction) where the denominator is not zero. Let's evaluate each of the given numbers:

1. √72 - This is not a rational number because it cannot be expressed as a fraction of two integers. Its decimal representation is approximately 8.49 (a non-repeating, non-terminating decimal).

2. 11/23 - This is a rational number because it is expressed as a fraction of two integers.

3. √14 - This is not a rational number because it cannot be expressed as a fraction of two integers. Its decimal representation is approximately 3.74 (a non-repeating, non-terminating decimal).

4. √36 - This is a rational number because it equals 6, which can be expressed as 6/1 (an integer divided by an integer).

5. 2.7 - This is a rational number because it can be expressed as 27/10 (a fraction).

6. π - This is not a rational number; it is an irrational number as it cannot be expressed as a fraction of two integers.

The three numbers that are rational from the list are:

• 11/23
• √36
• 2.7