# Such A Long sequence

Algebra Level 4

$$\large \frac{1}{3\sqrt1+\sqrt3}+\frac{1}{5\sqrt3+3\sqrt5}...........+\frac{1}{225\sqrt{223}+223\sqrt{225}} = ?$$

If this sum can be represented as $$\frac{a}{b}$$ , where both $$a,b$$ are square free and positive integers, find $$\large(ab)$$ if the operation $$\large(ab)$$ is defined as $$\large b \pmod{a}$$.

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