How to find an irrational number in between two given numbers like 2 &2.5?
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You can try $\displaystyle \sqrt{\frac{a^2+b^2}{2}}$.
Note that $\displaystyle a+b\sqrt{2}$ is always irrational provided that a and b are rational. As a result $\displaystyle 1+\sqrt{2}$ fits nicely.
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