$\sqrt{ }$ s Can Ruin Your Lives!

$\large \displaystyle \lim_{x \rightarrow 1} \frac{\sqrt{f(x)} - 1}{\sqrt{x} - 1}$

Multiplying top and bottom by $(\sqrt{x}+1)(\sqrt{f(x)}+1)$ ,

$\large \displaystyle \lim_{x-1 \rightarrow 0} \frac{f\left(x\right)-1}{x-1} \times \lim_{x \rightarrow 1} \frac{\sqrt{\left(x\right)}+1}{\sqrt{f\left(x\right)}+1}$

$\large \displaystyle \lim_{x-1 \rightarrow 0} \frac{f\left(x\right)-1}{x-1} \times \frac{\sqrt{\left(1\right)}+1}{\sqrt{f\left(1\right)}+1}$

Let $x-1=h$ , then:

$\large \displaystyle \lim_{h \rightarrow 0} \frac{f\left(1+h\right)-f\left(1\right)}{h} \times \frac{1+1}{1+1}$

$f'(1) \times 1 = \boxed{2}$

Why it is written (give your answer in 3 decimal places??😂)