Question 21
Find the value of the positive integer $n$ if
$$\frac1{\sqrt4+\sqrt5}+\frac1{\sqrt5+\sqrt6}+\frac1{\sqrt6+\sqrt7}+\cdots+\frac1{\sqrt n+\sqrt{n+1}}=10.$$
$$\frac1{\sqrt4+\sqrt5}+\frac1{\sqrt5+\sqrt6}+\frac1{\sqrt6+\sqrt7}+\cdots+\frac1{\sqrt n+\sqrt{n+1}}=10.$$