Which numbers are irrational? Check the three that apply.

Question

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(3 points)
Responses

16−−√
square root of 16

π
pi

12−−√
square root of 12

1.7
1 point 7

80−−√
square root of 80

718
7 over 18

Answer 1

To determine which numbers are irrational, we need to identify numbers that cannot be expressed as a simple fraction (i.e., the ratio of two integers). Here’s the classification of the options given:

1. √16: This is 4, which is a rational number.
2. π (pi): This is a well-known irrational number, as it cannot be expressed as a fraction of two integers.
3. √12: This can be simplified to 2√3. Since √3 is irrational, √12 is also irrational.
4. 1.7: This is a terminating decimal and can be expressed as a fraction (17/10), so it is rational.
5. √80: This can be simplified to 4√5. Since √5 is irrational, √80 is also irrational.
6. 7/18: This is a simple fraction and hence rational.

Based on this analysis, the irrational numbers from the list are:

• π
• √12
• √80

Therefore, the three numbers that apply are π, √12, and √80.