Which numbers are irrational? Check the three that apply.

Question

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(3 points)
Square root of 16

7/18

Square root of 80

Square root of 12

1.7

Pi

Answer 1

To identify the irrational numbers from the list provided, let's briefly define what an irrational number is:

An irrational number is a number that cannot be expressed as a simple fraction (i.e., the ratio of two integers). Its decimal representation goes on forever without repeating.

Now, let's evaluate each of the numbers:

1. Square root of 16: This equals 4, which is a rational number.

2. 7/18: This is a fraction of two integers, and thus it is a rational number.

3. Square root of 80: This simplifies to \( \sqrt{16 \cdot 5} = 4\sqrt{5} \), which is irrational because \( \sqrt{5} \) is an irrational number.

4. Square root of 12: This simplifies to \( \sqrt{4 \cdot 3} = 2\sqrt{3} \), which is also irrational because \( \sqrt{3} \) is irrational.

5. 1.7: This is a terminating decimal, which means it can be expressed as a fraction (17/10), making it a rational number.

6. Pi (π): This is a well-known irrational number.

Based on this evaluation, the irrational numbers from your list are:

• Square root of 80
• Square root of 12
• Pi

So, the three you would check are:

• Square root of 80
• Square root of 12
• Pi