Question

Rút gọn biểu thức:

Answer 1

Lời giải:
\(\sqrt{19+\sqrt{136}}-\sqrt{19-\sqrt{136}}=\sqrt{19+2\sqrt{34}}-\sqrt{19-2\sqrt{34}}\)

\(=\sqrt{17+2\sqrt{2.17}+2}-\sqrt{17-2\sqrt{17.2}+2}=\sqrt{(\sqrt{17}+\sqrt{2})^2}-\sqrt{(\sqrt{17}-\sqrt{2})^2}\)

\(=|\sqrt{17}+\sqrt{2}|-|\sqrt{17}-\sqrt{2}|=2\sqrt{2}\)

Answer 2

a) Ta có: \(\sqrt{19+\sqrt{136}}-\sqrt{19-\sqrt{136}}\)

\(=\sqrt{19+2\cdot\sqrt{34}}-\sqrt{19-2\sqrt{34}}\)

\(=\sqrt{17}+\sqrt{2}-\sqrt{17}+\sqrt{2}\)

\(=2\sqrt{2}\)