Sum of $\frac1{\sqrt1+\sqrt3}+\frac1{\sqrt5+\sqrt7}+...+\frac1{\sqrt{9997}+\sqrt{9999}}>24$

Question

Prove the following inequality. $\frac1{\sqrt1+\sqrt3}+\frac1{\sqrt5+\sqrt7}+...+\frac1{\sqrt{9997}+\sqrt{9999}}>24$

I tried to rationalizing the denominator and I got the following inequality to be proved,

$$-\sqrt1+\sqrt3-\sqrt5+\sqrt7-...-\sqrt{9997}+\sqrt{9999}>48$$

Once I got that, I don't know what to do with the LHS. Hints or solution would be appreciated.