\(\dfrac{1}{2}\sqrt{48}-2\sqrt{75}-\dfrac{\sqrt{33}}{\sqrt{11}}+5\sqrt{1\dfrac{1}{3}}\)
\(=2\sqrt{3}-10\sqrt{3}-\sqrt{3}+5\sqrt{\dfrac{4}{3}}\)
\(=2\sqrt{3}-10\sqrt{3}-\sqrt{3}+5\cdot\dfrac{2}{\sqrt{3}}\)
\(=2\sqrt{3}-10\sqrt{3}-\sqrt{3}+\dfrac{10}{\sqrt{3}}\)
\(=2\sqrt{3}-10\sqrt{3}-\sqrt{3}+\dfrac{10\sqrt{3}}{3}\)
\(=-\dfrac{17\sqrt{3}}{3}\)
Ta có: \(B-\dfrac{1}{3}=\dfrac{\sqrt{x}+1}{\sqrt{x}+3}-\dfrac{1}{3}=\dfrac{3\sqrt{x}+3-\sqrt{x}-3}{3\left(\sqrt{x}+3\right)}=\dfrac{2\sqrt{x}}{3\left(\sqrt{x}+3\right)}\)Vì x > 0 \(\Rightarrow2\sqrt{x}>0;3\left(\sqrt{x}+3\right)>0\Rightarrow\dfrac{2\sqrt{x}}{3\left(\sqrt{x}+3\right)}>0\)
\(\Rightarrow B-\dfrac{1}{3}>0\Rightarrow B>\dfrac{1}{3}\)
Bài 6:Cho \(B=\left(\dfrac{x+3}{x-9}+\dfrac{1}{\sqrt{x}+3}\right):\dfrac{\sqrt{x}}{\sqrt{x}-3}\left(x>0;x\ne9\right)\)
a) Rút gọn B
b) Tính B khi \(x=\sqrt{27+10\sqrt{2}}-\sqrt{18+8\sqrt{2}}\)
c) CMR \(B>\dfrac{1}{3}\)
Bài 7: Tính
1) \(\sqrt{12}-\sqrt{27}+18\sqrt{\dfrac{1}{3}}\)
2) \(\left(\sqrt{2}-\sqrt{3}\right)\left(\sqrt{8}+\sqrt{3}-1\right)\)
3) \(\dfrac{1}{\sqrt{5}-3}-\dfrac{1}{\sqrt{5}+3}\)
Bài 8: Phân tích thành tích
1) \(x-\sqrt{x}-12\)
2) \(x-5\sqrt{x}+4\)
3) \(3x-5\sqrt{x}-8\)
4) \(\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)-\sqrt{x}+1\)
5) \(x+3\left(\sqrt{x}+1\right)-1\)
6) \(\sqrt{x-1}-\sqrt{\sqrt{x-1}}\)
