Find a rational number between $\sqrt{2}$ and $\sqrt{3}$.

Consider the squares of $\sqrt{2}$ and $\sqrt{3}$

${(\sqrt2)^2}$ = 2 and ${(\sqrt3)^2}$ = 3

Take any rational number between 2 and 3 which is a perfect squares of a rational number,

One such number is 2.25 and

2.25 = $(1.5)^2$

$\sqrt{2.25}$ = 1.5

As, $2 \lt 2.25 \lt 3$ , it follows that

$\sqrt{2} \lt \sqrt{2.25} \lt \sqrt{3}$

$\sqrt{2} \lt 1.5 \lt \sqrt{3}$

Hence , one rational number between $\sqrt{2}$ and $\sqrt{3}$ is 1.5 .