Insert three irrational numbers between $2\sqrt{3}$ and $2\sqrt{5}$ , and arrange in descending order.

Consider the squares of $2\sqrt{3}$ and $2\sqrt{5}$.

$(2\sqrt{3})^2$ = 4 × 3 = 12 and $(2\sqrt{5})^2$ = 4 × 5 = 20

As , $18 \gt 17 \gt 15$ it follows that

$\sqrt{18} \gt \sqrt{17} \gt \sqrt{15}$ , therefore

$\sqrt{18}$ , $\sqrt{17}$ , $\sqrt{15}$ lie between $\sqrt{12}$ and $\sqrt{20}$ i.e. $2\sqrt{3}$ and $2\sqrt{5}$.

Hence, three irrational number between $2\sqrt{3}$ and $2\sqrt{5}$ in descending order are $\sqrt{18}$ , $\sqrt{17}$ , $\sqrt{15}$.