What least value should be added to $2505$ so that it becomes a perfect square?

If $a$ and $b$ are rational numbers and $(a-1) \sqrt{2} + 3 = b \sqrt{2} + a$,then the value of $(a+b)$ is

The value of $\frac{1}{a^{2}+a x+x^{2}}-\frac{1}{a^{2}-a x+x^{2}}+\frac{2 a x}{a^{4}+a^{2} x^{2}+x^{4}}$ is

The value of $\frac{1}{2} + \frac{1}{2 \cdot 3} + \frac{1}{2 \cdot 3 \cdot 4} + \frac{1}{2 \cdot 3 \cdot 4 \cdot 5}$ is correct to three places of decimal:

$1 \frac{4}{7} + 1 \frac{3}{5} + 1 \frac{1}{3} = ?$

Simplify:
$\frac{a^{1 / 2}+a^{-1 / 2}}{1-a}+\frac{1-a^{-1 / 2}}{1+\sqrt{a}}$