Question

Rút Gọn

a. \(\sqrt{3-\sqrt{ }5}:\sqrt{2}\)

b. \(\dfrac{\sqrt{8-4\sqrt{3}}}{\sqrt{ }2}\)

Answer 1

\(a,\sqrt{3-\sqrt{5}}:\sqrt{2}\)

=\(\dfrac{\sqrt{3-\sqrt{5}}.\sqrt{2}}{\sqrt{2}.\sqrt{2}}=\dfrac{\sqrt{6-2\sqrt{5}}}{2}=\dfrac{\sqrt{\left(\sqrt{5}-1\right)^2}}{2}=\dfrac{\sqrt{5}-1}{2}\)

Answer 2

a: \(=\sqrt{\dfrac{3-\sqrt{5}}{2}}=\sqrt{\dfrac{6-2\sqrt{5}}{4}}=\dfrac{\sqrt{5}-1}{\sqrt{2}}\)

b: \(=\sqrt{\dfrac{8-4\sqrt{3}}{2}}=\sqrt{\dfrac{6-2\cdot\sqrt{6}\cdot\sqrt{2}+2}{2}}\)

\(=\dfrac{\sqrt{6}-\sqrt{2}}{\sqrt{2}}=\sqrt{3}-1\)