a) \(\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}\)
\(=\sqrt{\left(\sqrt{3}\right)^2+2\sqrt{6}+\left(\sqrt{2}\right)^2}-\sqrt{\left(\sqrt{3}\right)^2-2\sqrt{6}+\left(\sqrt{2}\right)^2}\)
\(=\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}-\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}\)
\(=\sqrt{3}+\sqrt{2}-\left(\sqrt{3}-\sqrt{2}\right)=2\sqrt{2}\)
b) Tương tự
b) \(\sqrt{7-2\sqrt{10}}\) - \(\sqrt{7+2\sqrt{10}}\)
= \(\sqrt{\left(\sqrt{5}\right)^2-2\sqrt{5}.\sqrt{2}+\left(\sqrt{2}\right)^2}\) - \(\sqrt{\left(\sqrt{5}\right)^2+2\sqrt{5}.\sqrt{2}+\left(\sqrt{2}\right)^2}\)
= \(\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}\) - \(\sqrt{\left(\sqrt{5}+\sqrt{2}\right)^2}\)
= \(\left(\sqrt{5}-\sqrt{2}\right)\) - \(\left(\sqrt{5}+\sqrt{2}\right)\)
= \(\sqrt{5}-\sqrt{2}-\sqrt{5}-\sqrt{2}\)
= \(-2\sqrt{2}\)
