\(=\dfrac{\sqrt{15}\left(\sqrt{3}-1\right)}{\sqrt{27}\left(1-\sqrt{3}\right)}+\dfrac{-5-2\sqrt{2}}{17}\)
\(=-\sqrt{\dfrac{15}{27}}-\dfrac{5}{17}-\dfrac{2\sqrt{2}}{17}\)
\(=-\dfrac{\sqrt{5}}{3}-\dfrac{5}{17}-\dfrac{2\sqrt{2}}{17}=\dfrac{-17\sqrt{5}-15-6\sqrt{2}}{51}\)
thực hiện phép tính:
1, \(\dfrac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}-\dfrac{5-2\sqrt{5}}{2\sqrt{5}-4}\)
2,\(\dfrac{\sqrt{3}+1}{\sqrt{3}-1}+\dfrac{\sqrt{3}-1}{\sqrt{3}+1}\)
3,\(\dfrac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}+\dfrac{\sqrt{5}+\sqrt{27}}{\sqrt{30}-\sqrt{2}}\)
4,\(\dfrac{3-\sqrt{3}}{2\sqrt{3}-1}+\dfrac{3+\sqrt{3}}{2\sqrt{3}-1}\)
5,\(\dfrac{2\sqrt{3}-4}{\sqrt{3}-1}+\dfrac{2\sqrt{2}-1}{\sqrt{2}-1}-\dfrac{1+\sqrt{6}}{\sqrt{2}+\sqrt{3}}\)
1)\(\sqrt{12}\)\(-\)\(\sqrt{27}\)\(+\)\(\sqrt{48}\)
2)(\(\sqrt{24}+\sqrt{20}-\sqrt{80}\))\(\div\)5
3)2\(\sqrt{27}-\sqrt{\dfrac{16}{3}}\)\(-\)\(\sqrt{48}-\)\(\sqrt{8\dfrac{1}{3}}\)
4) \(\dfrac{1}{\sqrt{5}-\sqrt{3}}\)\(-\)\(\dfrac{1}{\sqrt{5+\sqrt{3}}}\)
Thực hiện các phép tính:
a. \(\left(\sqrt{80}+\sqrt{20}\right):\sqrt{45}\)
b. \(\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{18}+\sqrt{27}\right)\)
c. \(\dfrac{5\sqrt{3}-3\sqrt{5}}{\sqrt{5}-\sqrt{3}}-\dfrac{6}{\sqrt{15+3}}\)
d. \(\left(\sqrt{10+2\sqrt{21}}-\sqrt{10-2\sqrt{21}}\right)-\dfrac{4}{\sqrt{3}+1}\)
Thực hiện phép tính:
a. \(2\sqrt{16}+\sqrt{2}.\sqrt{0,02}-\dfrac{\sqrt{12,1}}{\sqrt{0,1}}\)
b. \(5\sqrt{20}-4\sqrt{45}+\dfrac{15}{\sqrt{5}}\)
c. \(\left(\dfrac{\sqrt{6}-\sqrt{3}}{5\sqrt{2}-5}+\dfrac{\sqrt{5}}{5}\right):\dfrac{2}{\sqrt{5}-\sqrt{3}}\)
d. \(\dfrac{\sqrt{6}-3}{\sqrt{3}-\sqrt{2}}-\dfrac{4}{\sqrt{3}+1}+3\sqrt{3}\)
\(\sqrt{3+2\sqrt{2}}-\sqrt{3-2\sqrt{2}}\)
\(\dfrac{1}{\sqrt{3}-1}-\dfrac{1}{\sqrt{3}+1}\)
\(2\sqrt{5}-3\sqrt{45}+\sqrt{500}\)
\(\dfrac{1}{\sqrt{3}+\sqrt{2}}-\dfrac{\sqrt{15}-\sqrt{12}}{\sqrt{5}-2}\)
\(\dfrac{1}{2+\sqrt{3}}-\dfrac{1}{2-\sqrt{3}}+5\sqrt{3}\)
\(\sqrt{3}-\sqrt{4+2\sqrt{3}}\)
\(\dfrac{5-\sqrt{5}}{\sqrt{5}-1}-\dfrac{4}{\sqrt{5}+1}\)
\(\sqrt{37-20\sqrt{3}+\sqrt{37+20\sqrt{3}}}\)
Thực hiện các phép tính:
a. \(2\sqrt{16}+\sqrt{2}.\sqrt{0.02}-\dfrac{\sqrt{12,1}}{\sqrt{0,1}}\)
b. \(5\sqrt{20}-4\sqrt{45}+\dfrac{15}{\sqrt{5}}\)
c. \(\left(\dfrac{\sqrt{6}-\sqrt{3}}{5\sqrt{2}-5}+\dfrac{\sqrt{5}}{5}\right):\dfrac{2}{\sqrt{5}-\sqrt{3}}\)
d. \(\dfrac{\sqrt{6}-3}{\sqrt{3}-\sqrt{2}}-\dfrac{4}{\sqrt{3}+1}+3\sqrt{3}\)
Rút gọn:
a) \(2\sqrt{98}-3\sqrt{18}+\dfrac{1}{2}\sqrt{32}\)
b)\(\left(5\sqrt{2}+2\sqrt{5}\right).\sqrt{5}-\sqrt{250}\)
c)\(\left(2\sqrt{3}-5\sqrt{2}\right).\sqrt{3}-\sqrt{36}\)
d)\(3\sqrt{48}+2\sqrt{27}-\dfrac{1}{3}\sqrt{243}\)
e) \(6\sqrt{\dfrac{1}{3}}+\dfrac{9}{\sqrt{3}}-\dfrac{2}{\sqrt{3}-1}\)
f)\(4\sqrt{\dfrac{1}{2}}-\dfrac{6}{\sqrt{2}}\dfrac{2}{\sqrt{2}+1}\)
Thực hiện các phép tính sau:
a. \(\dfrac{5\sqrt{3}-3\sqrt{5}}{\sqrt{5}-\sqrt{3}}-\dfrac{6}{\sqrt{15}+3}\)
b. \(\left(\sqrt{10+2\sqrt{21}}-\sqrt{10-2\sqrt{21}}\right)-\dfrac{4}{\sqrt{3}+1}\)
c. \(\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{18}+\sqrt{27}\right)\)
1/Tính
A=\(\dfrac{\sqrt{15-10\sqrt{2}}+\sqrt{13+4\sqrt{10}}-\sqrt{11+2\sqrt{10}}}{2\sqrt{3+2\sqrt{2}}+\sqrt{9-4\sqrt{2}}+\sqrt{12+8\sqrt{2}}}\)
B=\(\dfrac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2}+\sqrt{3}}+\dfrac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2}-\sqrt{3}}\)
C=\(\dfrac{\sqrt{2-\sqrt{3}}+\sqrt{4-\sqrt{15}}+\sqrt{10}}{\sqrt{23-3\sqrt{5}}}\)
D=\(\dfrac{\sqrt{4+\sqrt{3}}+\sqrt{4-\sqrt{3}}}{\sqrt{4+\sqrt{13}}}\)
2/So sánh
\(\sqrt{2017^2-1}-\sqrt{2016^2-1}\) và \(\dfrac{2.1016}{\sqrt{2017^2-1}+\sqrt{2016^2-1}}\)
