Câu a : \(\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}\)
\(=\sqrt{2+2.\sqrt{2}.\sqrt{3}+3}-\sqrt{2-2.\sqrt{2}.\sqrt{3}+3}\)
\(=\sqrt{\left(\sqrt{2}+\sqrt{3}\right)^2}-\sqrt{\left(\sqrt{2}-\sqrt{3}\right)^2}\)
\(=\left|\sqrt{2}+\sqrt{3}\right|-\left|\sqrt{2}-\sqrt{3}\right|\)
\(=\sqrt{2}+\sqrt{3}-\sqrt{3}+\sqrt{2}\)
\(=2\sqrt{2}\)
Câu b : \(\sqrt{7-2\sqrt{10}}-\sqrt{7+2\sqrt{10}}\)
\(=\sqrt{2-2.\sqrt{2}.\sqrt{5}+5}-\sqrt{2+2.\sqrt{2}.\sqrt{5}+5}\)
\(=\sqrt{\left(\sqrt{2}-\sqrt{5}\right)^2}-\sqrt{\left(\sqrt{2}+\sqrt{5}\right)^2}\)
\(=\left|\sqrt{2}-\sqrt{5}\right|-\left|\sqrt{2}+\sqrt{5}\right|\)
\(=\sqrt{5}-\sqrt{2}-\sqrt{2}-\sqrt{5}\)
\(=-2\sqrt{2}\)
a, \(\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}=\sqrt{2+2.\sqrt{2}.\sqrt{3}+3}-\sqrt{2-2\sqrt{2}.\sqrt{3}+3}\)
\(=\sqrt{\left(\sqrt{2}+\sqrt{3}\right)^2}-\sqrt{\left(\sqrt{2}-\sqrt{3}\right)^2}\)\(=\sqrt{2}+\sqrt{3}-\left(\sqrt{3}-\sqrt{2}\right)\)\(=2\sqrt{2}\)
\(b,\sqrt{7-2\sqrt{10}}-\sqrt{7+2\sqrt{10}}=\sqrt{\left(\sqrt{5}+\sqrt{2}\right)^2}-\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}\)
\(=\sqrt{5}+\sqrt{2}-\sqrt{5}+\sqrt{2}=2\sqrt{2}\)
