e) \(\dfrac{3}{5}\sqrt{150x}-2\sqrt{216x}+3\sqrt{54x}\)
\(=\dfrac{3}{5}\sqrt{25\cdot6x}-2\sqrt{36\cdot6x}+3\sqrt{9\cdot6x}\)
\(=\dfrac{3}{5}\cdot5\sqrt{6x}-2\cdot6\sqrt{6x}+3\cdot3\sqrt{6x}\)
\(=3\sqrt{6x}-12\sqrt{6x}+9\sqrt{6x}\)
\(=\left(3-12+9\right)\sqrt{6x}\)
\(=\sqrt{6x}\cdot0\)
\(=0\)
f) \(5\sqrt{a}-4b\sqrt{25a^3}+5a\sqrt{16ab^2}-2\sqrt{9a}\)
\(=5\sqrt{a}-4b\cdot5a\sqrt{a}+5a\cdot4b\sqrt{a}-2\cdot3\sqrt{a}\)
\(=5\sqrt{a}-20ab\sqrt{a}+20ab\sqrt{a}-6\sqrt{a}\)
\(=\left(5-6\right)\sqrt{a}\)
\(=-\sqrt{a}\)
e: \(=\dfrac{3}{5}\cdot5\sqrt{6x}-2\cdot6\sqrt{6x}+3\cdot3\sqrt{6x}\)
\(=3\sqrt{6x}-12\sqrt{6x}+9\sqrt{6x}=0\)
f: \(=5\sqrt{a}-6\sqrt{a}-4b\cdot5a\sqrt{a}+5a\cdot4b\sqrt{a}\)
\(=-\sqrt{a}\)
