Question

A=\(\sqrt{5-2\sqrt{6}}\)

B=\(\sqrt{7+2\sqrt{10}}+\sqrt{7-2\sqrt{10}}\)

C= \(\sqrt{8+2\sqrt{15}}-\sqrt{5}\)

Answer 1

\(A=\sqrt{5-2\sqrt{6}}=\sqrt{3-2\sqrt{3}.\sqrt{2}+2}=\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}=\sqrt{3}-\sqrt{2}\) \(B=\sqrt{7+2\sqrt{10}}+\sqrt{7-2\sqrt{10}}=\sqrt{5+2\sqrt{5}.\sqrt{2}+2}+\sqrt{5-2.\sqrt{5}.\sqrt{2}+2}=\sqrt{\left(\sqrt{5}+\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}=2\sqrt{5}\) \(C=\sqrt{8+2\sqrt{15}}-\sqrt{5}=\sqrt{5+2\sqrt{5}.\sqrt{3}+3}-\sqrt{5}=\sqrt{5}+\sqrt{3}-\sqrt{5}=\sqrt{3}\)