Question

Tính giá trị cuả biểu thức:

\(\sqrt{2+\sqrt{3}}\)

Answer 1

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

Answer 2

Đặt A= \(\sqrt{2+\sqrt{3}}\)

\(\Leftrightarrow A\sqrt{2}=\sqrt{4+2\sqrt{3}}\)

\(\Leftrightarrow A\sqrt{2}=\sqrt{3+2\sqrt{3}+1}\)

\(\Leftrightarrow A\sqrt{2}=\sqrt{\left(\sqrt{3}+1\right)^2}\)

\(\Leftrightarrow A\sqrt{2}=\sqrt{3}+1\)

\(\Rightarrow A=\dfrac{\sqrt{3}+1}{\sqrt{2}}\)