Rút gọn biểu thức: \(5a\sqrt{64ab^{3}}-\sqrt{3}\cdot \sqrt{12a^{3}b^{3}}+2ab\sqrt{9ab}-5b\sqrt{81a^{3}b}.\) với \(a>0, b>0\)

* Hướng dẫn giải

Ta có:

\(5a\sqrt{64ab^{3}}-\sqrt{3}.\sqrt{12a^{3}b^{3}}+2ab\sqrt{9ab}-5b\sqrt{81a^{3}b}\)

\(=5a\sqrt{8^2.b^2.ab}-\sqrt{3}.\sqrt{2^2.3.(ab)^2.ab}\)\(\,+2ab\sqrt{3^2.ab}-5b\sqrt{9^2.a^2.ab}\)

\(=5a\sqrt{(8b)^2.ab}-\sqrt{3}.\sqrt{(2ab)^2.3.ab}+2ab\sqrt{3^2.ab}\)\(\,-5b\sqrt{(9a)^2.ab}\)

\(=5a.8b\sqrt{ab}-\sqrt{3}.2\sqrt 3 ab\sqrt{ab}+2ab.3\sqrt{ab}\)\(\,-5b.9a\sqrt{ab}\)

\(=40ab\sqrt{ab}-2.3ab\sqrt{ab}+6ab\sqrt{ab}-45ab\sqrt{ab}\)

\(=40ab\sqrt{ab}-6ab\sqrt{ab}+6ab\sqrt{ab}-45ab\sqrt{ab}\)

\(=40ab\sqrt{ab}-45ab\sqrt{ab}\)

\(=(40-45)ab\sqrt{ab}\)

\(=-5ab\sqrt{ab}\).