Question

Rút gọn A=\(\dfrac{\sqrt{2-\sqrt{3}}}{\sqrt{2}}\)

Answer 1

\(A=\dfrac{\sqrt{2-\sqrt{3}}}{\sqrt{2}}\\ =\dfrac{\sqrt{\left(2-\sqrt{3}\right).2}}{2}\\ =\dfrac{\sqrt{4-2\sqrt{3}}}{2}\\ =\dfrac{\sqrt{\left(1-\sqrt{3}\right)^2}}{2}\\ =\dfrac{\sqrt{3}-1}{2}\)

Answer 2

\(A=\dfrac{\sqrt{2}\cdot\sqrt{2-\sqrt{3}}}{2}=\dfrac{\sqrt{4-2\sqrt{3}}}{2}=\dfrac{\sqrt{\left(\sqrt{3}-1\right)^2}}{2}=\dfrac{\sqrt{3}-1}{2}\)