Question

If $\sqrt{2}$=1.4142, then find the value of $\frac{\sqrt{2}-1}{\sqrt{2}+1}$

Answer 1

$\sqrt{2}=1.4142\frac{\sqrt{2}-1}{\sqrt{2}+1}=\frac{(\sqrt{2}-1)}{(\sqrt{2}+1)}\times \frac{(\sqrt{2}-1)}{\sqrt{2}-1}$
(Ragionalization)
$=\frac{(\sqrt{2}-1{)}^2}{2-1}=\frac{1+1-2\sqrt{2}}{1}=3-2\sqrt{2}=3-2\left(1.4142\right)=3-2.8284=0.1716$