Question:
How many irrational numbers lie between $\sqrt{2}$ and $\sqrt{3}$ ? Find any three irrational numbers lying between $\sqrt{2}$ and $\sqrt{3}$.
Solution:
There are infinite number of irrational numbers lying between $\sqrt{2}$ and $\sqrt{3}$.
As, $\sqrt{2}=1.414$ and $\sqrt{3}=1.732$
So, the three irrational numbers lying between $\sqrt{2}$ and $\sqrt{3}$ are:
1.420420042000..., 1.505005000... and 1.616116111...
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