How to treat small number within square root guys.I am reading a math book. It has a equation shown as follows,
$\sqrt{(1+\Delta^2)}$
And then,since $\Delta$ is very small, it can be written as,
$\sqrt{(1+\Delta^2)} = (1+\frac12\Delta^2)$
What is the theory behind this equation?

What @Mohamed_Fadel noted is NOT true.
The correct taylor expansion for $\sqrt {1+x^2}$ at the point $x_0=0$ is:
$$\sqrt {1+x^2} = 1 + \frac {1}{2} x^2 - \frac {1}{8} x^4 + \frac {1}{16} x^6...$$
That you get by just going through the standard taylor expansion.
For getting $\sqrt{(1+\Delta^2)} = (1+\frac12\Delta^2)$, all you need to do is neglect every order following the quadratic.
@Mohamed_Fadel: You cannot treat $x^2$ like a single variable $x$ when expanding, because inner derivatives will arise when doing the Taylor expansion.
