Question:
A rational number between $\sqrt{2}$ and $\sqrt{3}$ is
(a) $\frac{\sqrt{2}+\sqrt{3}}{2}$
(b) $\frac{\sqrt{2} \cdot \sqrt{3}}{2}$
(c) $1.5$
(d) $1.8$
Solution:
(c)
A rational number between $(\sqrt{2}$ and $\sqrt{3})$ i.e., $1.414$ and $1.732$.
(a) $\frac{\sqrt{2}+\sqrt{3}}{2}$, which is an irrational number, so it is not a solution.
(b) $\frac{\sqrt{2} \cdot \sqrt{3}}{2}=\frac{\sqrt{6}}{2}$, which is an irrational number, so it is not a solution.
Now, $1.5$ and $1.8$ both are the rational numbers but only $1.5$ lies between $1.414$ and $1.732$.
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