a) Ta có:
\(5\sqrt{a}-4b\sqrt{25a^{3}}+5a\sqrt{16ab^{2}}-2\sqrt{9a}\)
\(=5\sqrt a - 4b\sqrt{5^2.a^2.a}+5a\sqrt{4^2.b^2.a}-2\sqrt{3^2.a}\)
\(=5\sqrt a - 4b\sqrt{(5a)^2.a}+5a\sqrt{(4b)^2.a}-2\sqrt{3^2.a}\)
\(=5\sqrt a - 4b.5a\sqrt{.a}+5a.4b\sqrt{a}-2.3\sqrt{a}\)
\(=5\sqrt{a}-20ab\sqrt{a}+20ab\sqrt{a}-6\sqrt{a}\)
\(=(5\sqrt{a}-6\sqrt{a})+(-20ab\sqrt{a}+20ab\sqrt{a})\)
\(=(5-6)\sqrt a=-\sqrt{a}\)
b) Ta có:
\(5a\sqrt{64ab^{3}}-\sqrt{3}.\sqrt{12a^{3}b^{3}}+2ab\sqrt{9ab}-5b\sqrt{81a^{3}b}\)
\(=5a\sqrt{8^2.b^2.ab}-\sqrt{3}.\sqrt{2^2.3.(ab)^2.ab}\)\(\,+2ab\sqrt{3^2.ab}-5b\sqrt{9^2.a^2.ab}\)
\(=5a\sqrt{(8b)^2.ab}-\sqrt{3}.\sqrt{(2ab)^2.3.ab}+2ab\sqrt{3^2.ab}\)\(\,-5b\sqrt{(9a)^2.ab}\)
\(=5a.8b\sqrt{ab}-\sqrt{3}.2\sqrt 3 ab\sqrt{ab}+2ab.3\sqrt{ab}\)\(\,-5b.9a\sqrt{ab}\)
\(=40ab\sqrt{ab}-2.3ab\sqrt{ab}+6ab\sqrt{ab}-45ab\sqrt{ab}\)
\(=40ab\sqrt{ab}-6ab\sqrt{ab}+6ab\sqrt{ab}-45ab\sqrt{ab}\)
\(=40ab\sqrt{ab}-45ab\sqrt{ab}\)
\(=(40-45)ab\sqrt{ab}\)
\(=-5ab\sqrt{ab}\).
