Question

rút gọn căn thức

a)\(\frac{1}{\sqrt{3}-\sqrt{5}}.\sqrt{\frac{10\sqrt{3}-6\sqrt{5}}{5\sqrt{3}+3\sqrt{5}}}\)

Answer 1

\(=\frac{1}{\sqrt{3}-\sqrt{5}}\cdot\sqrt{\frac{2\sqrt{15}\left(\sqrt{5}-\sqrt{3}\right)}{\sqrt{15}\left(\sqrt{5}+\sqrt{3}\right)}}\) \(=\frac{1}{\sqrt{3}-\sqrt{5}}\cdot\sqrt{\frac{2\left(\sqrt{5}-\sqrt{3}\right)^2}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}}\)

\(=\frac{1}{\sqrt{3}-\sqrt{5}}\cdot\sqrt{\frac{2\left(\sqrt{5}-\sqrt{3}\right)^2}{5-3}}\)\(=\frac{1}{\sqrt{3}-\sqrt{5}}\cdot\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}\)

\(=\frac{1}{\sqrt{3}-\sqrt{5}}\cdot\left(\sqrt{5}-\sqrt{3}\right)=-1\)