Question

If $\sqrt{2}=1.414$, then find the value of $\frac{1}{3+\sqrt{2}}$.

Answer 1

$\frac{1}{3+\sqrt{2}}$

$=\frac{3-\sqrt{2}}{(3{)}^2-(\sqrt{2}{)}^2}$

$=\frac{3-\sqrt{2}}{7}$

$=\frac{1.586}{7}$

$=0.2266$ [ taking approximation upto four decimal places]