Which numbers are irrational? Check the three that apply. NOTE: There is a check answer button in the bottom right corner. Click this to check your answer before moving on to the next question. It will not tell you the correct answer, but it will tell you if the answer you selected is correct. You can use this feature once per question.(3 points)Responsesπpi7187 over 1880−−√square root of 8016−−√square root of 1612−−√square root of 121.71 point 7

Answer 1

To determine which numbers are irrational among the options provided, we need to recall that an irrational number cannot be expressed as a fraction of two integers and its decimal form is non-repeating and non-terminating.

Let's analyze the given numbers:

1. π (pi): This is a well-known irrational number, as it cannot be expressed as a fraction of two integers.

2. \( \frac{718}{1880} \): This is a fraction, and thus it is a rational number. It can be expressed as two integers with a numerator and denominator.

3. \( \sqrt{80} \): The square root of 80 can be simplified to \( \sqrt{16 \times 5} = 4\sqrt{5} \). Since \( \sqrt{5} \) is irrational, \( \sqrt{80} \) is also irrational.

4. \( \sqrt{16} \): This equals 4, which is a rational number because it can be expressed as \( \frac{4}{1} \).

5. \( \sqrt{12} \): The square root of 12 can be simplified to \( \sqrt{4 \times 3} = 2\sqrt{3} \). Since \( \sqrt{3} \) is irrational, \( \sqrt{12} \) is also irrational.

6. 1.7: This is a terminating decimal and can be expressed as a fraction \( \frac{17}{10} \), making it a rational number.

Based on this analysis, the irrational numbers from the provided options are:

• π
• \( \sqrt{80} \)
• \( \sqrt{12} \)

So, the correct choices are: π, \( \sqrt{80} \), \( \sqrt{12} \).