Kind find the limit of the following question

Question

What is the limit of the following? lim(h->0) ((2+h)^0.5 -(2)^0.5)/h

Note: I'm struggling to make the denominator positive.

Answer 1

First way:

$$\lim_{h\to 0}\frac{\sqrt{2+h}-\sqrt2}h=(\sqrt x)'|_{x=2}=\frac1{2\sqrt2}$$

Second way:

$$\lim_{h\to 0}\frac{\sqrt{2+h}-\sqrt2}h=\frac{2+h-2}{h(\sqrt{2+h}+\sqrt2)}=\frac1{\sqrt{2+h}+\sqrt2}\xrightarrow[h\to 0]{}\frac1{2\sqrt2}$$