Question

Find two irrational numbers between 5 and 6.

Answer 1

Since 5 and 6 are rational numbers and $5\times 6=30$ is not a perfect square.

$\therefore$ One irrational number between 5 and 6 is $\sqrt{5\times 6}=\sqrt{30}$

And, an irrational number between 5 and $\sqrt{30}=\sqrt{5\times \sqrt{30}}=\sqrt{5\sqrt{30}}$