A rational number between

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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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