1.a) \(3\sqrt{18}-\sqrt{50}-5\sqrt{72}+2\sqrt{98}=3\sqrt{9.2}-\sqrt{25.2}-5\sqrt{36.2}+2\sqrt{49.2}\)
\(=9\sqrt{2}-5\sqrt{2}-30\sqrt{2}+14\sqrt{2}=-12\sqrt{2}\)
b) \(2\sqrt{45}-\sqrt{12}-3\sqrt{80}+4\sqrt{27}=2\sqrt{9.5}-\sqrt{4.3}-3\sqrt{16.5}+4\sqrt{9.3}\)
\(=6\sqrt{5}-2\sqrt{3}-12\sqrt{5}+12\sqrt{3}=10\sqrt{3}-6\sqrt{5}\)
c) \(\left(5\sqrt{2}-2\sqrt{5}\right)^2=\left(5\sqrt{2}\right)^2-2.5\sqrt{2}.2\sqrt{5}+\left(2\sqrt{5}\right)^2\)
\(=50-20\sqrt{10}+20=70-20\sqrt{10}\)
d) \(\dfrac{1}{\sqrt{3}-\sqrt{2}}+\dfrac{3}{\sqrt{2}+\sqrt{5}}\)
\(=\dfrac{\sqrt{3}+\sqrt{2}}{\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)}+\dfrac{3\left(\sqrt{5}-\sqrt{2}\right)}{\left(\sqrt{2}+\sqrt{5}\right)\left(\sqrt{5}-\sqrt{2}\right)}\)
\(=\sqrt{3}+\sqrt{2}+\dfrac{3\left(\sqrt{5}-\sqrt{2}\right)}{3}=\sqrt{3}+\sqrt{2}+\sqrt{5}-\sqrt{2}=\sqrt{3}+\sqrt{5}\)
2. \(A=\dfrac{\sqrt{x}-2}{\sqrt{x}+5}=\dfrac{\sqrt{x}+5-7}{\sqrt{x}+5}=1-\dfrac{7}{\sqrt{x}+5}\)
Để \(A\in Z\Rightarrow\sqrt{x}+5\inƯ\left(7\right)\) mà \(\sqrt{x}+5\ge5\Rightarrow\sqrt{x}+5=7\Rightarrow\sqrt{x}=2\)
\(\Rightarrow x=4\)