An example of irrational numbers is

the square root of -17
square root of 16
square root of -9***
square root of 1

An irrational number cannot be expressed as a ratio between two numbers and it cannot be written as a simple fraction because there is not a finite number of numbers when written as a decimal. Instead, the numbers in the decimal would go on forever, without repeating.

None of the above are irrational numbers.

irrationals are a subset of the reals
-17 and -9 do not have real square roots
16 and 1 are perfect squares, so their roots are integers

I suspect a typo. Irrationals are things like
√17, π, etc.

Answer is square root of -17!!

Ah, irrational numbers, the rebels of the number world! While the square root of -17 and the square root of -9 seem flabbergasting on the surface, they actually belong to the mystical realm of complex numbers. So, they can't be considered irrational numbers. However, the square root of 16 and the square root of 1 are pretty chill and rational. So, they don't fit the bill either. Keep searching for that quirky irrational number, my friend!

An example of an irrational number is the square root of -9. To determine whether a number is rational or irrational, we need to understand the properties of each.

A rational number can be expressed as a fraction of two integers. For example, 4 can be written as 4/1, and 0.5 can be written as 1/2. Rational numbers can be written as terminating decimals (such as 0.25) or repeating decimals (such as 0.3333...).

On the other hand, an irrational number cannot be expressed as a fraction of two integers. Irrational numbers are typically written as non-repeating, non-terminating decimals. They cannot be simplified or expressed as a precise fraction.

Let's go through the examples you provided:

1. The square root of -17: This is an example of an imaginary number. It cannot be expressed as a real number because the square root of a negative number does not exist in the set of real numbers. However, if we include imaginary numbers, the square root of -17 is √(-17), which can be written as 4.123105625617661j (using the "j" notation to indicate an imaginary number).

2. The square root of 16: This is a rational number. The square root of 16 is 4, which can be expressed as a fraction: 4/1. It is also a terminating decimal.

3. The square root of -9: This is another example of an imaginary number. The square root of -9 is √(-9), which can be written as 3j.

4. The square root of 1: This is a rational number. The square root of 1 is 1, which can be expressed as a fraction: 1/1. It is also a terminating decimal.

To summarize, out of the examples you provided, the square roots of -17 and -9 are examples of irrational numbers, while the square roots of 16 and 1 are examples of rational numbers.