\(A=\frac{3}{\sqrt{7}-2}-\frac{14}{\sqrt{7}}+\sqrt{\left(\sqrt{7}-2\right)^2}\)
\(=\frac{3\left(\sqrt{7}+2\right)}{3}-\frac{14\sqrt{7}}{7}+\sqrt{7}-2\)
\(=\sqrt{7}+2-2\sqrt{7}+\sqrt{7}-2\)
\(=0\)
rút gọn biểu thức
a) \(\frac{3}{2+\sqrt{3}}+\frac{13}{4-\sqrt{3}}+\frac{6}{\sqrt{3}}\)
b) \(\left(\frac{\sqrt{14}-\sqrt{7}}{\sqrt{2}-1}+\frac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}\right):\frac{1}{\sqrt{7}-\sqrt{5}}\)
c) \(\sqrt{\left(2+\sqrt{3}\right)^2}-\sqrt{28-10\sqrt{3}}\)
d) \(\frac{3}{3+2\sqrt{3}}+\frac{3}{3-2\sqrt{3}}\)
e) \(\sqrt{20}-15\sqrt{\frac{1}{5}}+\sqrt{\left(1-\sqrt{5}\right)^2}\)
Bài 1: Tính
1, \(A=\left(1-\frac{5+\sqrt{5}}{1+\sqrt{5}}\right).\left(\frac{5-\sqrt{5}}{1-\sqrt{5}}-1\right)\)
2, \(B=\left(\frac{3\sqrt{125}}{15}-\frac{10-4\sqrt{6}}{\sqrt{5}-2}\right).\frac{1}{\sqrt{5}}\)
3, \(C=\left(\frac{\sqrt{1000}}{100}-\frac{5\sqrt{2}-2\sqrt{5}}{2\sqrt{5}-8}\right).\frac{\sqrt{10}}{10}\)
4, \(D=\frac{1}{\sqrt{49+20\sqrt{6}}}-\frac{1}{\sqrt{49-20\sqrt{6}}}+\frac{1}{\sqrt{7-4\sqrt{3}}}\)
5, \(E=\frac{1}{\sqrt{4-2\sqrt{3}}}-\frac{1}{\sqrt{7-\sqrt{48}}}+\frac{3}{\sqrt{14-6\sqrt{5}}}\)
6, \(F=\frac{1}{\sqrt{2}-\sqrt{3}}\sqrt{\frac{3\sqrt{2}-2\sqrt{3}}{3\sqrt{2}+2\sqrt{3}}}\)
7, \(G=\frac{\sqrt{15-10\sqrt{2}}+\sqrt{13+4\sqrt{10}-\sqrt{11-2\sqrt{10}}}}{2\sqrt{3+2\sqrt{2}}+\sqrt{9-4\sqrt{2}+\sqrt{12+8\sqrt{2}}}}\)
1) \(\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}-\sqrt{5}}+\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}\)
2) \(x+2y-\sqrt{\left(x^2-4xy+4y^2\right)^2\left(x\ge2y\right)}\)
3) 4x + \(\sqrt{\left(x-12\right)^2}\left(x\ge2\right)\)
Tinh
\(a,\sqrt{75}-\sqrt{5\frac{1}{3}}+\frac{9}{2}\sqrt{2\frac{2}{3}}+2\sqrt{27}\)
\(b,\sqrt{48}+\sqrt{5\frac{1}{3}}+2\sqrt{75}-5\sqrt{1\frac{1}{3}}\)
\(c,\left(\sqrt{15}+2\sqrt{3}\right)^2+12\sqrt{5}\)
\(d,\left(\sqrt{6}+2\right)\left(\sqrt{3}-\sqrt{2}\right)\)
\(e,\left(\sqrt{3}+1\right)^2-2\sqrt{3}+4\)
\(f,\frac{1}{7+4\sqrt{3}}+\frac{1}{7-4\sqrt{3}}\)
\(g,\left(\frac{1}{\sqrt{5}-\sqrt{2}}-\frac{1}{\sqrt{5}+\sqrt{2}}+1\right)\frac{1}{\left(\sqrt{2}+1\right)^2}\)
Rút gọn biểu thức:
1) \(\sqrt{\left(1-\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{2}+3\right)^2}\)
2) \(\sqrt{\left(\sqrt{3}-2\right)^2}+\sqrt{\left(\sqrt{3}-1\right)^2}\)
3) \(\left(\sqrt{19}-3\right)\left(\sqrt{19}+3\right)\)
4) \(4x+\sqrt{\left(x-12\right)^2}\left(x\ge2\right)\)
5) \(\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}-\sqrt{5}}+\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}\)
6) \(x+2y-\sqrt{\left(x^2-4xy+4y^2\right)^2}\left(x\ge2y\right)\)
\(\left(\frac{a+\sqrt{a}}{\sqrt{a+1}}-\frac{\sqrt{a}-1}{a-\sqrt{a}}\right):\frac{\sqrt{a}-1}{a}\)
\(\sqrt{\left(2+\sqrt{7}\right)^2}-\sqrt{\left(2-\sqrt{7}\right)^2}\)
Rút gọn :
M = \(\frac{1}{3.\left(\sqrt{1}+\sqrt{2}\right)}+\frac{1}{5.\left(\sqrt{2}+\sqrt{3}\right)}+\frac{1}{7.\left(\sqrt{3}+\sqrt{4}\right)}+....+\frac{1}{49.\left(\sqrt{24}+\sqrt{25}\right)}\)
Bài 1 : Cho A=\(\left(\frac{\sqrt{14}-\sqrt{7}}{\sqrt{2}-1}+\frac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}\right):\frac{1}{\sqrt{7}-\sqrt{5}}\)
B=\(\frac{1}{x+\sqrt{x}}-\frac{1}{x-\sqrt{x}}+\frac{2\sqrt{x}}{x-1}\)
a) Rút gọn A và B
b) tìm x để A > B
Bài 1 :
a, \(\sqrt{45}-2\sqrt{\frac{4}{3}}+\frac{\sqrt{18}}{\sqrt{6}}-\sqrt{5\frac{1}{3}}\)
b, (\(\sqrt{7}-\sqrt{3}\) )2 +\(\sqrt{84}\)
Bài 2 : Chứng minh đẳng thức
\(\left(\frac{\sqrt{21}-\sqrt{7}}{\sqrt{3}-1}\frac{\sqrt{15}+\sqrt{3}}{\sqrt{5}+1}\right):\frac{1}{\sqrt{7}+\sqrt{3}}=4\)
Bài 3: Cho biểu thức : A=\(\left(1-\frac{2\sqrt{2a}}{a+2}\right):\left(\frac{1}{\left(\sqrt{a}+2\right)}-\frac{2\sqrt{2a}}{\left(a+2\right)\left(\sqrt{a}+2\right)}\right)\)
a. Rút gọn A
b. Tính A khi a =2009-2\(\sqrt{2008}\)
Bài 4 : Cho A =\(\left(1-\frac{4}{\sqrt{x}+1}+\frac{1}{x-1}\right):\frac{x-2\sqrt{x}}{x-1}\) điều kiện x>0 , x≠1,x≠4
a.Rút gọn
b. Tìm x để A =\(\frac{1}{2}\)
