Rút gọn biểu thức sau: \(\sqrt{18(\sqrt{2}-\sqrt{3})^{2}}\)

* Hướng dẫn giải

Ta có:

\(\sqrt{18(\sqrt{2}-\sqrt{3})^{2}}=\sqrt {18}.\sqrt{(\sqrt 2 - \sqrt 3)^2}\)

\(=\sqrt{9.2}.|\sqrt{2}-\sqrt{3}|=\sqrt{3^2.2}.|\sqrt{2}-\sqrt{3}|\)

\(=3\sqrt{2}.|\sqrt{2}-\sqrt{3}|=3\sqrt{2}(\sqrt{3}-\sqrt{2})\)

\(=3\sqrt {2.3}- 3(\sqrt 2)^2\)

\(=3\sqrt 6 -3.2=3\sqrt{6}-6\).

(Vì  \( 2 < 3 \Leftrightarrow \sqrt 2 < \sqrt 3 \Leftrightarrow \sqrt 2 -\sqrt 3 <0\)

Do đó: \( |\sqrt 2 -\sqrt 3|=-(\sqrt 2 -\sqrt 3)=-\sqrt 2 +\sqrt 3\)\(=\sqrt 3-\sqrt2\)).