Question

Rút gọn các căn thức sau

\(\sqrt{12-3\sqrt{7}}\)

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

\(\sqrt{3-\sqrt{5}}\)

\(\sqrt{7-3\sqrt{5}}\)

Answer 1

\(\sqrt{\frac{24-6\sqrt{7}}{2}}=\sqrt{\frac{\left(\sqrt{21}-\sqrt{3}\right)^2}{2}}=\frac{\sqrt{21}-\sqrt{3}}{\sqrt{2}}=\frac{\sqrt{42}-\sqrt{6}}{2}\)

\(\sqrt{2-\sqrt{3}}=\sqrt{\frac{4-2\sqrt{3}}{2}}=\sqrt{\frac{\left(\sqrt{3}-1\right)^2}{2}}=\frac{\sqrt{3}-1}{\sqrt{2}}=\frac{\sqrt{6}-\sqrt{2}}{2}\)

\(\sqrt{\frac{6-2\sqrt{5}}{2}}=\sqrt{\frac{\left(\sqrt{5}-1\right)^2}{2}}=\frac{\sqrt{10}-\sqrt{2}}{2}\)

\(\sqrt{\frac{14-6\sqrt{5}}{2}}=\sqrt{\frac{\left(3-\sqrt{5}\right)^2}{2}}=\frac{3\sqrt{2}-\sqrt{10}}{2}\)