Question

Tính \(\sqrt{2+\sqrt{3}}\)

Answer 1

\(A=\sqrt[]{2+\sqrt{3}}\Rightarrow\sqrt{2}A=\sqrt{4+2\sqrt{3}}=\sqrt{\left(\sqrt{3}+1\right)^2}=\sqrt{3}+1\Rightarrow A=\dfrac{\sqrt{3}+1}{\sqrt{2}}\)

Answer 2

\(\sqrt{2+\sqrt{3}}\approx1,931\)

Answer 3

\(\sqrt{2+\sqrt{3}}=\dfrac{1}{\sqrt{2}}\sqrt{4+2\sqrt{3}}=\dfrac{1}{\sqrt{2}}\sqrt{\left(\sqrt{3}+1\right)^2}=\dfrac{\sqrt{3}+1}{\sqrt{2}}=\dfrac{\sqrt{6}+\sqrt{2}}{2}\)