Question

Insert five irrational numbers between $2\sqrt{5}$ and $\sqrt{3}.$

Answer 1

$2\sqrt{5}=\sqrt{4\times 5}=\sqrt{20}$
$3\sqrt{3}=\sqrt{9\times 3}=\sqrt{27}$
Hence five irrational numbers between $\sqrt{20}$ and $\sqrt{27}$ can be $\sqrt{21},\sqrt{22},\sqrt{23},\sqrt{24}$ and $\sqrt{25}$