Question

[Đỗ Hà My]

\(\sqrt{193-132\sqrt{2}}+\sqrt{193+132\sqrt{2}}\)
giúp mình với mng ơi

Answer 1

[Đoàn Đức Hà]

\(\sqrt{193-132\sqrt{2}}+\sqrt{193+132\sqrt{2}}=\sqrt{121-2.11.6\sqrt{2}+72}+\sqrt{121+2.11.6\sqrt{2}+72}\)

\(=\sqrt{11^2-2.11.6\sqrt{2}+\left(6\sqrt{2}\right)^2}+\sqrt{11^2+2.11.6\sqrt{2}+\left(6\sqrt{2}\right)^2}\)

\(=\sqrt{\left(11-6\sqrt{2}\right)^2}+\sqrt{\left(11+6\sqrt{2}\right)^2}=\left|11-6\sqrt{2}\right|+\left|11+6\sqrt{2}\right|\)

\(=11-6\sqrt{2}+11+6\sqrt{2}=22\)

Answer 2

[Lê Nguyễn Huyền Anh]

p/s : cách khác 

Đặt \(Nghia=\sqrt{193-132\sqrt{2}}+\sqrt{193+132\sqrt{2}}\)

\(\Rightarrow Nghia^2=193-132\sqrt{2}+193+132\sqrt{2}+2\sqrt{\left(193-132\sqrt{2}\right)\left(193+132\sqrt{2}\right)}\)

\(=386+2\sqrt{2401}=386+2.49=484\)

\(\Rightarrow Nghia=\sqrt{484}=22\)