bằng 4,877630889.10^-4
Rút gọn mà . Ai nói dùng máy
Đặt \(A=\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
\(\Rightarrow A^2=4+\sqrt{10+2\sqrt{5}}+2\sqrt{\left(4+\sqrt{10+2\sqrt{5}}\right)\left(4-\sqrt{10+2\sqrt{5}}\right)}+4-\sqrt{10+2\sqrt{5}}\)
\(=8+2\sqrt{16-10-2\sqrt{5}}\)
\(=8+2\sqrt{6-2\sqrt{5}}\)
\(=8+2\sqrt{\left(\sqrt{6}-1\right)^2}\)
\(=8+2\left(\sqrt{6}-1\right)\)
\(=6+2\sqrt{6}\)
\(\Rightarrow A=\sqrt{6+2\sqrt{6}}\)
\(\sqrt{5}\)chứ ko phải \(\sqrt{6}\)nha