Tính :

a ) \(S=\frac{1}{\sqrt{1}\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{7}}+.....+\)\(\frac{1}{\sqrt{2017}+\sqrt{2019}}\)

b ) \(S=\frac{1}{\sqrt{2}+\sqrt{4}}+\frac{1}{\sqrt{4}+\sqrt{6}}+....+\frac{1}{\sqrt{100}+\sqrt{102}}\)

c ) \(S=\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+.....+\frac{1}{\sqrt{100}+\sqrt{101}}\)

d  ) \(S=\frac{1}{\sqrt{3}+\sqrt{6}}+\frac{1}{\sqrt{6}+\sqrt{9}}+\frac{1}{\sqrt{9}+\sqrt{12}}+....+\frac{1}{\sqrt{2016}+\sqrt{2019}}\)

bài 1 thực hiện các phép tính sau:

a) \(\sqrt{12}+2\sqrt{27}+3\sqrt{75}-9\sqrt{48}\)

b)\(2\sqrt{2}-\sqrt{3^2}\)

c) \(\left(\sqrt{x}-3\right)\left(4-\sqrt{x}\right)\)

bài 2 rút gọn biểu thức sau:

a)\(\frac{\sqrt{15}-\sqrt{6}}{\sqrt{35}-\sqrt{14}}\)

b)\(\frac{2\sqrt{15}-2\sqrt{10}+\sqrt{6}-3}{2\sqrt{5}-2\sqrt{10}-\sqrt{3}+\sqrt{6}}\)

c)\(\frac{\sqrt{10}+\sqrt{15}}{\sqrt{8}+\sqrt{12}}\)

d)\(\frac{x-2\sqrt{x}}{x+4-4\sqrt{x}}\)

bài 1: rút gọn các biểu thúc sau

a, \(\frac{\sqrt{1-2x+x^2}}{x-1}\)

b, \(\frac{\sqrt{\left(x-3\right)^2}}{3-x}\)

c, \(\frac{\sqrt{9x^2-6x+1}}{9x^2-1}\)

d, 4-x-\(\sqrt{4-4x+x^2}\)

bài 2 rút gọn

a, \(\frac{\sqrt{6}+\sqrt{10}}{\sqrt{21}+\sqrt{35}}\)

b, \(\frac{\sqrt{405+3\sqrt{27}}}{3\sqrt{3}+\sqrt{45}}\)

c, \(\frac{\sqrt{2}+\sqrt{3}+\sqrt{4}-\sqrt{6}-\sqrt{9}-\sqrt{12}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)

d, \(\frac{\sqrt{6-2\sqrt{5}}}{\sqrt{5}-1}\)

Rút gọn biểu thức

A = \(\frac{\sqrt{3}+\sqrt{11+6\sqrt{2}}-\sqrt{5+2\sqrt{6}}}{\sqrt{2}+\sqrt{6+2\sqrt{5}}-\sqrt{7+2\sqrt{10}}}\)

B = \(\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)

C = \(\sqrt{2-\sqrt{3}}-\sqrt{2+\sqrt{3}}\)

D = \(\sqrt{28+6\sqrt{3}}-\sqrt{28-6\sqrt{3}}\)

E = \(6x+\sqrt{9x^2-12x+4}\)

F = \(5x-\sqrt{x^2+4x+4}\)