Question

rút gọn biểu thức:

\(\sqrt{8+4\sqrt{3}}-\sqrt{9-6\sqrt{2}}\)

Answer 1

Lời giải:
\(\sqrt{8+4\sqrt{3}}-\sqrt{9-6\sqrt{2}}=\sqrt{6+2+2\sqrt{6}.\sqrt{2}}-\sqrt{6+3-2\sqrt{6}.\sqrt{3}}\)

\(=\sqrt{(\sqrt{6}+\sqrt{2})^2}-\sqrt{(\sqrt{6}-\sqrt{3})^2}\)

\(=\sqrt{6}+\sqrt{2}-(\sqrt{6}-\sqrt{3})=\sqrt{2}+\sqrt{3}\)