Let f (x) = $\sqrt{x}$
Now, $f(x+\delta x)-f\left(x\right)=f^{\prime }\left(x\right).\delta x=\frac{\delta x}{2\sqrt{x}}$
We may write, 25.2 = 25 + 0.2
Taking x = 25 and $\delta x=0.2$ We have
$f\left(25.2\right)-f\left(25\right)=\frac{0.2}{2\sqrt{25}}=0.02\therefore f\left(25.2\right)=f\left(25\right)+0.02=\sqrt{25}+0.02=5.02\Rightarrow \sqrt{\left(25.2\right)}=5.02$