# What are three irrational numbers between 2 and 3?

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Please see below.

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Powers of

and powers of

Hence

as

For other ways of finding such numbers see What are three numbers between 0.33 and 0.34?

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Adding on to the other answer, we can easily generate as many such numbers as we'd like by noting that the sum of an irrational with a rational is irrational. For example, we have the well known irrationals

So, without worrying about the exact bounds, we can definitely add any positive number less than

This can be done with any irrational for which we have an approximation for at least the integer portion. For example, we know that

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Irrational numbers are those that never give a clear result. Three of those between

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Irrational numbers are always approximations of a value, and each one tends to go on forever. Roots of all numbers that are *not perfect squares* (NPS) are irrational, as are some useful values like

To find the irrational numbers between two numbers like *squares* of the two numbers which in this case are

Now we know that the start and end points of our set of possible solutions are *squaring* is how we found them.

Then using the definition above, we can say that the root of all NPS numbers between the two squares we just found will be irrational numbers between the original numbers. Between

The roots of these will be irrational numbers between

Eg: *approximately*, or, we will never have the exact numerical answer.

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