Question

thực hiện phép tính

M=\(\sqrt{9+4\sqrt{5}}-\sqrt{9-4\sqrt{5}}\)

Answer 1

ta có : \(M=\sqrt{9+4\sqrt{5}}-\sqrt{9-4\sqrt{5}}=\sqrt{\left(\sqrt{5}+2\right)^2}+\sqrt{\left(\sqrt{5}-2\right)^2}\)

\(\left|\sqrt{5}+2\right|+\left|\sqrt{5}-2\right|=\sqrt{5}+2+\sqrt{5}-2=2\sqrt{5}\)

Answer 2

\(M=\sqrt{9+4\sqrt{5}}-\sqrt{9-4\sqrt{5}}=\sqrt{5+2.2\sqrt{5}+4}-\sqrt{5-2.2\sqrt{5}+4}=\sqrt{\left(\sqrt{5}+2\right)^2}-\sqrt{\left(\sqrt{5}-2\right)^2}=\sqrt{5}+2-\sqrt{5}+2=4\)