Question

Find 3 irrational numbers between and using their decimal expansion.

Hard

Solution

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The decimal expansions of and  are as follows:
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Here, the one decimal expansions are non-terminating recurring, while the other is terminating.
Hence,  and  are two rational numbers.

We know, between any two rational numbers, there are infinitely many irrational numbers.
An irrational number has non-terminating non-recurring decimal expansions.

Then different irrational number between  and  can be:


Here we observe that .

NOTE:
This is of the various possible answers. It might have different solution.

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