Chương I - Căn bậc hai. Căn bậc ba
Các câu hỏi tương tự
Cho E= \(\dfrac{1+xy}{x+y} - \dfrac{1-xy}{x-y} \)
Biết x= \(\sqrt{4+\sqrt{8}} . \sqrt{2+\sqrt{2 + \sqrt{2}}} . \sqrt{2 -\sqrt{2 +\sqrt{2}}}\)
y =\(\dfrac{ 3 \sqrt{8} -2 \sqrt{12}+ \sqrt{20}}{ 3\sqrt{18} -2\sqrt{27} + \sqrt{45}}\)
\(A=\frac{8}{4+2\sqrt{x}}-\frac{2-\sqrt{x}}{4-x}\)
\(B=\frac{x\sqrt{y}+y\sqrt{x}}{\sqrt{xy}}:\frac{1}{\sqrt{x}-\sqrt{y}}-x\)
THỰC HIỆN PHÉP TÍNH:
22) frac{1}{sqrt{5}+sqrt{2}}+frac{1}{sqrt{5}-sqrt{2}}
23) frac{2+sqrt{3}}{sqrt{2}+sqrt{2+sqrt{3}}}+frac{2-sqrt{3}}{sqrt{2}-sqrt{2-sqrt{3}}}
24) frac{sqrt{18}}{sqrt{2}}-frac{sqrt{12}}{sqrt{3}}
25) sqrt{left(sqrt{5}+1right)^2}+sqrt{left(sqrt{5}-1right)^2}
27) sqrt{3-2sqrt{2}}
28) frac{1}{sqrt{8}+sqrt{7}}+sqrt{175}-2sqrt{2}
30) left(2sqrt{1frac{9}{16}}-sqrt{5frac{1}{16}}right):sqrt{16}
34) frac{left(5sqrt{3}+sqrt{50}right)left(5-sqrt{24}right)}{sqrt{75}-5sqrt{2}}
35) l...
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THỰC HIỆN PHÉP TÍNH:
22) \(\frac{1}{\sqrt{5}+\sqrt{2}}+\frac{1}{\sqrt{5}-\sqrt{2}}\)
23) \(\frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
24) \(\frac{\sqrt{18}}{\sqrt{2}}-\frac{\sqrt{12}}{\sqrt{3}}\)
25) \(\sqrt{\left(\sqrt{5}+1\right)^2}+\sqrt{\left(\sqrt{5}-1\right)^2}\)
27) \(\sqrt{3-2\sqrt{2}}\)
28) \(\frac{1}{\sqrt{8}+\sqrt{7}}+\sqrt{175}-2\sqrt{2}\)
30) \(\left(2\sqrt{1\frac{9}{16}}-\sqrt{5\frac{1}{16}}\right):\sqrt{16}\)
34) \(\frac{\left(5\sqrt{3}+\sqrt{50}\right)\left(5-\sqrt{24}\right)}{\sqrt{75}-5\sqrt{2}}\)
35) \(\left(2\sqrt{6}-4\sqrt{3}+5\sqrt{2}-\frac{1}{4}\sqrt{8}\right).3\sqrt{6}\)
36) \(\frac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\frac{\sqrt{5}+\sqrt{27}}{\sqrt{30}+\sqrt{162}}\)
39) \(\sqrt{\frac{2-\sqrt{3}}{2+\sqrt{3}}+\sqrt{\frac{2+\sqrt{3}}{2-\sqrt{3}}}}\)
45) \(\frac{\sqrt{6-2\sqrt{5}}}{2-\sqrt{20}}\)
Rút gọn:
a,\(\frac{3+\sqrt{3}}{1+\sqrt{3}}\)
b,\(\frac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-\sqrt{2}}\)
c,\(\frac{y-2\sqrt{y}}{\sqrt{y}-2}\)
d,\(\frac{x+2\sqrt{x}-3}{\sqrt{x}-1}\)
e,\(\frac{4y+3\sqrt{y}-7}{4\sqrt{y}+7}\)
g,\(\frac{x-3\sqrt{x}-4}{x-\sqrt{x}-12}\)
P = \(\frac{x}{\sqrt{xy}+y}+\frac{y}{\sqrt{xy}-x}-\frac{x+y}{\sqrt{xy}}
\)
a) Rút gọn P
b) Tính Pkhi x = \(\sqrt{2-\sqrt{3}}\); y = \(\sqrt{2+\sqrt{3}}\)
Cho A= \(\frac{\sqrt{x}}{\sqrt{xy}+\sqrt{x}+2}+\frac{\sqrt{y}}{\sqrt{yz}+\sqrt{y}+1}+\frac{2\sqrt{z}}{\sqrt{zx}+2\sqrt{z}+2}\)
Biết xyz=4. Tính \(\sqrt{A}\)
Bài tập:Rút gọn
1.frac{sqrt{2}+sqrt{3}+sqrt{6}+sqrt{8}+4}{sqrt{2}+sqrt{3}+sqrt{4}}
2. 2sqrt{27}-6sqrt{frac{4}{3}}+frac{3}{5}sqrt{75}
3. 8sqrt{3}-2sqrt{25sqrt{12}}+4sqrt{sqrt{192}}
4.frac{1}{2+sqrt{3}}+frac{sqrt{2}}{sqrt{6}}-frac{2}{3+sqrt{3}}
5.(sqrt{12}+sqrt{75}+sqrt{27}):sqrt{15}
6.frac{1}{2}sqrt{48}-2sqrt{75}-frac{sqrt{33}}{sqrt{11}}+5sqrt{1frac{1}{3}}
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Bài tập:Rút gọn
1.\(\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
2. \(2\sqrt{27}-6\sqrt{\frac{4}{3}}+\frac{3}{5}\sqrt{75}\)
3. \(8\sqrt{3}-2\sqrt{25\sqrt{12}}+4\sqrt{\sqrt{192}}\)
4.\(\frac{1}{2+\sqrt{3}}+\frac{\sqrt{2}}{\sqrt{6}}-\frac{2}{3+\sqrt{3}}\)
5.(\(\sqrt{12}+\sqrt{75}+\sqrt{27}\)):\(\sqrt{15}\)
6.\(\frac{1}{2}\sqrt{48}-2\sqrt{75}-\frac{\sqrt{33}}{\sqrt{11}}+5\sqrt{1\frac{1}{3}}\)
a) CMR: \(\frac{1}{\sqrt{a+3}+\sqrt{a+2}}+\frac{1}{\sqrt{a+2}+\sqrt{a+1}}+\frac{1}{\sqrt{a+1}+\sqrt{a}}=\frac{3}{\sqrt{a+3}+\sqrt{a}}\)
b) Cho các số thực dương x, y, z thỏa mãn x+y+z=1. CMR: \(\frac{x}{x+yz}+\frac{y}{y+xz}+\frac{z}{z+xy}\le\frac{9}{4}\)
Rút gọn:
\(A=\dfrac{x+y-2\sqrt{xy}}{\sqrt{x}-\sqrt{y}}-\dfrac{x+\sqrt{xy}}{\sqrt{x}+\sqrt{y}}\)
\(B=\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)