Insert two rational numbers and two irrational numbers between ${\sqrt3}$ and ${\sqrt8}$.

Since, square of ${\sqrt3}$ = 3 and square of ${\sqrt8}$ = 8.

(i) Choose any two rational numbers between 3 and 8 each of which is a perfect square.

The square roots of such numbers will be requires rational numbers.

Let the numbers be 4 and 5.76, where $\sqrt4$ = 2 and $\sqrt{5.76}$ = 2.4

∴ Required rational numbers are 2 and 2.4.

(ii) Now, choose any two rational numbers between 3 and 8 each of which is not a perfect square. The square root of such numbers will be the required irrational numbers.

Let the numbers be 5 and 6.

∴ $\sqrt{5}$ and $\sqrt{6}$ are the required irrational numbers.