Write three irrational numbers between $\sqrt{2} \text{ and } \sqrt{7}$

We want three irrational numbers between $\sqrt{2} \text{ and } \sqrt{7}$.

Consider any three numbers between 2 and 7 such that they are not perfect squares.

Let us take 3, 5 and 6 as they are not perfect squares.

We know that square root of a non-perfect square is an irrational number.

∴ $\sqrt{3}, \sqrt{5} \text{ and } \sqrt{6}$ are irrational numbers.

Thus, we have :

$\Rightarrow \sqrt{2} \lt \sqrt{3} \lt \sqrt{5} \lt \sqrt{6} \lt\sqrt{7}$

Hence, three irrational numbers between

$\sqrt{2} \text{ and } \sqrt{7} \text{ are } \sqrt{3}, \sqrt{5} \text{ and } \sqrt{6}$.