\(=\dfrac{\sqrt{12}\left(1-\sqrt{3}\right)}{\sqrt{8}\left(1-\sqrt{3}\right)}-1-\sqrt{3}+\dfrac{-2-2\sqrt{7}}{3}\)
\(=\dfrac{2\sqrt{3}}{2\sqrt{2}}+\dfrac{-3-3\sqrt{3}-2-2\sqrt{7}}{3}\)
\(=\dfrac{3\sqrt{6}}{6}-\dfrac{-10-6\sqrt{3}-4\sqrt{7}}{6}\)
\(=\dfrac{3\sqrt{6}+10+6\sqrt{3}+4\sqrt{7}}{6}\)
Tính
1, \(\dfrac{6}{1-\sqrt{3}}-\dfrac{3\sqrt{3}+3}{\sqrt{3}+1}\)
2, \(\dfrac{\sqrt{12}-6}{\sqrt{8}-\sqrt{24}}-\dfrac{3+\sqrt{3}}{\sqrt{3}}+\dfrac{4}{1-\sqrt{7}}\)
3, \(\left(\dfrac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}+\dfrac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\dfrac{1}{\sqrt{7}-\sqrt{5}}\)
4, \(\dfrac{\left(\sqrt{2}+1\right)^2-4\sqrt{2}}{\sqrt{2}-1}.\left(\sqrt{2}+1\right)\)
Giúp mìnk với nha mấy bạn///Thank kiu nhìu!!!
Tính giá trị các biểu thức sau
1.\(\dfrac{1}{\sqrt{1}-\sqrt{2}}-\dfrac{1}{\sqrt{2}-\sqrt{3}}+\dfrac{1}{\sqrt{3}-\sqrt{4}}-\dfrac{1}{\sqrt{4}-\sqrt{5}}+\dfrac{1}{\sqrt{5}-\sqrt{6}}-\dfrac{1}{\sqrt{6}-\sqrt{7}}+\dfrac{1}{\sqrt{7}-\sqrt{8}}-\dfrac{1}{\sqrt{8}-\sqrt{9}}\)
2.\(\dfrac{1}{2\sqrt{1}+1\sqrt{2}}+\dfrac{1}{3\sqrt{2}+2\sqrt{3}}+\dfrac{1}{4\sqrt{3}+3\sqrt{4}}+\dfrac{1}{5\sqrt{4}+4\sqrt{5}}+\dfrac{1}{6\sqrt{5}+5\sqrt{6}}+\dfrac{1}{7\sqrt{6}+6\sqrt{7}}\)
giúp mk vs ạ
So sánh:
a) \(4\sqrt{7}\) và \(3\sqrt{13}\)
b) \(3\sqrt{12}\) và \(2\sqrt{16}\)
c) \(\dfrac{1}{4}\sqrt{84}\) và \(6\sqrt{\dfrac{1}{7}}\)
d) \(3\sqrt{12}\) và \(2\sqrt{16}\)
e) \(\dfrac{1}{2}\sqrt{\dfrac{17}{2}}\) và \(\dfrac{1}{3}\sqrt{19}\)
rút gọn :
a)\(\left(\dfrac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}+\dfrac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}\right):\dfrac{1}{\sqrt{7}-\sqrt{5}}\)
b) \(\sqrt{\dfrac{3\sqrt{3}-4}{2\sqrt{3}+1}}+\sqrt{\dfrac{\sqrt{3}+4}{5-2\sqrt{3}}}\)
c) \(\dfrac{2\sqrt{5}-5\sqrt{2}}{\sqrt{2}-\sqrt{5}}+\dfrac{6}{2-\sqrt{10}}+\sqrt{67+12\sqrt{7}}\)
d) \(\left(\dfrac{\sqrt{5}}{\sqrt{2}+1}+\dfrac{14}{2\sqrt{2}-1}-\dfrac{6}{2-\sqrt{2}}\right).\sqrt{17-12\sqrt{2}}\)
Thực hiện phép tính
-\(\left(5+2\sqrt{6}\right)\left(49-20\sqrt{6}\right)\sqrt{5-2\sqrt{6}}\)
- \(\dfrac{1}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{1}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
-\(\dfrac{\left(5+\sqrt{2}\right)^2-8\sqrt{5}}{2\sqrt{5}-4}\)
- \(\sqrt{14-8\sqrt{3}}-\sqrt{24-12\sqrt{3}}\)
- \(\dfrac{\sqrt{3}}{1-\sqrt{\sqrt{3}+1}}+\dfrac{\sqrt{3}}{1+\sqrt{\sqrt{3}+1}}\)
Rút gọn:
A= \(\dfrac{1}{\sqrt{7-\sqrt{24}}+1}-\dfrac{1}{\sqrt{7+\sqrt{24}}+1}\)
B=\(\dfrac{2}{\sqrt{8-2\sqrt{5}}}-\dfrac{1}{\sqrt{5-2\sqrt{6}}}-\dfrac{3}{\sqrt{7+2\sqrt{10}}}\)
Rút gọn:
A = \(\dfrac{4+\sqrt{7}}{3\sqrt{2}+\sqrt{4+\sqrt{7}}}+\dfrac{4-\sqrt{7}}{3\sqrt{2}-\sqrt{4-\sqrt{7}}}\)
B = \(\dfrac{3\sqrt{2}+\sqrt{11}}{\sqrt{2}+\sqrt{6+\sqrt{11}}}+\dfrac{3\sqrt{2}-\sqrt{11}}{\sqrt{2}-\sqrt{6-\sqrt{11}}}+18\)
C = \(\dfrac{1}{\sqrt{3}+\sqrt{5}}+\dfrac{1}{\sqrt{5}+\sqrt{7}}+...+\dfrac{1}{\sqrt{2n+1}+\sqrt{2n+3}}\)với n thuộc N*
D = \(\left(\sqrt{3}+1\right)\left(\sqrt{5}-1\right)\left(\sqrt{15}-1\right)\left(7-2\sqrt{3}+\sqrt{5}\right)\)
E=\(\dfrac{\left(4+\sqrt{3}\right)}{\sqrt[]{1}+\sqrt{3}}+\dfrac{\left(8+\sqrt{15}\right)}{\sqrt{3}+\sqrt{5}}+...+\dfrac{2k+\sqrt{k^2-1}}{\sqrt{k-1}+\sqrt{k+1}}+...+\dfrac{240+\sqrt{14399}}{\sqrt{119}+\sqrt{121}}\)
F = \(\left(\dfrac{2a+1}{a\sqrt{a}-1}-\dfrac{\sqrt{a}}{a+\sqrt{a}+1}\right)\left(\dfrac{1+a\sqrt{a}}{1+\sqrt{a}}-\sqrt{a}\right)\) với a >= 0 và a khác 1
rg: \(\sqrt{\left(\sqrt{7}-4\right)}^2\) = 3
chứng minh:
\(\left(\sqrt{8}-5\sqrt{2}+\sqrt{20}\right)\sqrt{5}-\left(3\sqrt{\dfrac{1}{10}}+10\right)=3.3\sqrt{10}\)
\(\left(\sqrt{12}-6\sqrt{3}+\sqrt{24}\right)\sqrt{6}\left(5\sqrt{\dfrac{1}{2}}+12\right)=-14.5\sqrt{2}\)
rút gon bieu thức
\(\left(3\sqrt{2}+\sqrt{6}\right).\sqrt{6-3\sqrt{3}}\)
\(\sqrt{12-3\sqrt{7}}-\sqrt{12+3\sqrt{7}}\)
\(\sqrt{\dfrac{13}{4}+\sqrt{3}}-\sqrt{\dfrac{7}{4}-\sqrt{3}}\)
\(\sqrt{\dfrac{289+4\sqrt{72}}{16}}+\sqrt{\dfrac{129}{16}+\sqrt{2}}\)
\(\sqrt{11+6\sqrt{2}}-\sqrt{\sqrt{8}+3}\)
\(\sqrt{16-6\sqrt{7}}+\sqrt{10-2\sqrt{21}}\)
Thực hiện phép tính
a. 2\(\sqrt{\dfrac{16}{3}}\) - 3\(\sqrt{\dfrac{1}{27}}-6\sqrt{\dfrac{4}{75}}\)
b. \(\sqrt{\dfrac{2-\sqrt{3}}{2+\sqrt{3}}}+\sqrt{\dfrac{2+\sqrt{3}}{2-\sqrt{3}}}\)
c.\(2\sqrt{27}-6\sqrt{\dfrac{4}{3}}+\dfrac{3}{5}\sqrt{75}\)
d. \(\dfrac{1}{\sqrt{2}+\sqrt{2}+\sqrt{3}}+\dfrac{1}{\sqrt{2}-\sqrt{2}-\sqrt{3}}\)
e. \(\dfrac{\sqrt{3-\sqrt{5}}.\left(3+\sqrt{5}\right)}{\sqrt{10}+\sqrt{2}}\)
d. \(\sqrt{2-\sqrt{3}}\left(\sqrt{5}+\sqrt{2}\right)\)
e. \(\sqrt{14-8\sqrt{3}}-\sqrt{24-12\sqrt{3}}\)
g. \(\sqrt{4-\sqrt{9}+4\sqrt{2}}\)
