Question

Given root 2=1.414 find the value of 3+root 2/3-root 2

Answer 1

$$\begin{gathered} \frac{3+\sqrt{2}}{3-\sqrt{2}} \\ =\frac{3+\sqrt{2}}{3-\sqrt{2}}\times \frac{3+\sqrt{2}}{3+\sqrt{2}} \\ =\frac{{\left(3+\sqrt{2}\right)}^2}{{\left(3\right)}^2-{\left(\sqrt{2}\right)}^2} \\ =\frac{9+2+6\sqrt{2}}{9-2} \\ =\frac{11+6\sqrt{2}}{7} \\ =\frac{11+6\times 1.414}{7} \\ =\frac{19.484}{7} \\ =2.783 \end{gathered}$$