Question

If root3 = 1.73205, then what is the value of root of (Root 3 -1) / (Root 3 +1)

Answer 1

$$\begin{gathered} \frac{\sqrt{3}-1}{\sqrt{3}+1} \\ =\frac{\sqrt{3}-1}{\sqrt{3}+1}\times \frac{\sqrt{3}-1}{\sqrt{3}-1} \\ =\frac{{\left(\sqrt{3}-1\right)}^2}{{\left(\sqrt{3}\right)}^2-{\left(1\right)}^2} \\ =\frac{3+1-2\sqrt{3}}{3-1} \\ =\frac{4-2\sqrt{3}}{2} \\ =2-\sqrt{3} \\ =2-1.73205 \\ =0.26795 \end{gathered}$$