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

Question

Responses

1123
11 over 23

2.7
2 point 7

π
pi

72−−√
square root of 72

14−−√
square root of 14

36−−√

Answer 1

Rational numbers are those that can be expressed as the quotient (or fraction) of two integers, where the denominator is not zero. Let's analyze the options given:

1. 1123 - This is a whole number, and all whole numbers are rational (can be expressed as 1123/1). (Rational)

2. 11 over 23 - This is explicitly in the form of a fraction, where both the numerator (11) and the denominator (23) are integers. (Rational)

3. 2.7 - This is a decimal and can be expressed as 27/10, which is a fraction of two integers. (Rational)

4. π - This is an irrational number; it cannot be expressed as a fraction of two integers. (Not Rational)

5. 72−−√ - The square root of 72 is approximately 8.485, which cannot be expressed as a fraction of two integers (it is not a perfect square). (Not Rational)

6. 14−−√ - The square root of 14 is approximately 3.742, which also cannot be expressed as a fraction of two integers. (Not Rational)

7. 36−−√ - This equals 6, which is a whole number and thus rational (can be expressed as 6/1). (Rational)

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

• 1123
• 11 over 23
• 2.7
• 36−−√

So the three responses that apply are 1123, 11 over 23, and 2.7.