Thực hiện phép tính:

1)A=\(\left(\dfrac{1}{3-\sqrt{5}}-\dfrac{1}{3+\sqrt{5}}\right)\) . \(\dfrac{5-\sqrt{5}}{\sqrt{5}-1}\)

2)B = \(\dfrac{1}{1 +\sqrt{2}}\) +\(\dfrac{1}{\sqrt{2}+\sqrt{3}}\)+.....+\(\dfrac{1}{\sqrt{99}+\sqrt{100}}\)

3)C = \(\sqrt[3]{7+5\sqrt{2}}\) - \(\sqrt[3]{7-5\sqrt{2}}\)

4) D = \(\sqrt[3]{9+4\sqrt{5}}\)+\(\sqrt[3]{9-4\sqrt{3}}\)

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. \(\sqrt{4-\sqrt{9}+4\sqrt{2}}\)

D = \(\sqrt{94-42\sqrt{5}}-\sqrt{94+42\sqrt{5}}\)

A = \(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)

C = \(\dfrac{2\sqrt{4-\sqrt{5+\sqrt{21+\sqrt{80}}}}}{\sqrt{10}-\sqrt{2}}\)

F = \(\sqrt{2+\sqrt{3}}\cdot\sqrt{2+\sqrt{2+\sqrt{3}}\cdot\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}}\cdot\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}\)

B = \(\dfrac{1}{\sqrt{1}+\sqrt{2}}+\dfrac{1}{\sqrt{2}+\sqrt{3}}+\dfrac{1}{\sqrt{3}+\sqrt{4}}+...+\dfrac{1}{\sqrt{n-1}+\sqrt{n}}\)

E = \(\dfrac{1}{\sqrt{1}-\sqrt{2}}-\dfrac{1}{\sqrt{2}-\sqrt{3}}+\dfrac{1}{\sqrt{3}-\sqrt{4}}-...-\dfrac{1}{\sqrt{24}-\sqrt{25}}\)

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,\(\dfrac{2\sqrt{3}-4}{\sqrt{3}-1}+\dfrac{2\sqrt{2}-1}{\sqrt{2}-1}-\dfrac{1+\sqrt{6}}{\sqrt{2}+\sqrt{3}}\)

bài 1 :Trục căn thức ở mẫu và rút ngọn nếu được.

a) \(\dfrac{\sqrt{5}-\sqrt{3}}{\sqrt{2}}\) b) \(\dfrac{26}{5-2\sqrt{3}}\) c) \(\dfrac{9-2\sqrt{3}}{3\sqrt{6}-2\sqrt{2}}\)

d) \(\dfrac{2\sqrt{10}-5}{4-\sqrt{10}}\) g) \(\dfrac{\sqrt{3}}{\sqrt{\sqrt{3}+1}-1}-\dfrac{\sqrt{3}}{\sqrt{\sqrt{3}+1+1}}\)

bài 2: tính giá trị các biểu thức sau:

a)\(\dfrac{2}{\sqrt{7}-5}-\dfrac{2}{\sqrt{7}+5}\) b) \(\dfrac{\sqrt{7}+\sqrt{5}}{\sqrt{7}-\sqrt{5}}+\dfrac{\sqrt{7}-\sqrt{5}}{\sqrt{7}-\sqrt{5}}\)

c) \(\sqrt{12}+\sqrt{48}-\sqrt{(\sqrt{75}-\sqrt{108)}^2}\)

bài 3: thực hiện phép tính.

a) \(\sqrt{(3-2\sqrt{2})^2}+\sqrt{(3+2\sqrt{2})^2}\) b)\(\sqrt{(5-2\sqrt{6})^2}-\sqrt{(5+2\sqrt{6})^2}\)

c) \(\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}\) d) \(\sqrt{7-2\sqrt{10}}-\sqrt{7+2\sqrt{10}}\)

bài 4: thực hiện các phép tính sau.

a) \(\sqrt{125}-4\sqrt{45}+3\sqrt{20}-\sqrt{80}\) b) \(2\sqrt{\dfrac{27}{4}}-\sqrt{\dfrac{48}{9}}\dfrac{2}{5}\sqrt{\dfrac{75}{16}}\)

c) \(\sqrt{8}+\sqrt{72}+\sqrt{98}-5\sqrt{128}\) d) \(2\sqrt{\dfrac{9}{8}}-\sqrt{\dfrac{49}{2}}+\sqrt{\dfrac{25}{18}}\)

bài 5: rút ngọn biểu thức với giả thiết các biểu thức chữ đều có nghĩa.

a) \(\dfrac{x\sqrt{x}+y\sqrt{y}}{\sqrt{x}+\sqrt{y}}-\sqrt{xy}(x>0;y>0)\)

b) \(\dfrac{a+\sqrt{ab}}{b+\sqrt{ab}}(a;b\ge0)\)

bài 6: giải các phương trình sau:\(\dfrac{1}{2}\sqrt{x-1}-\dfrac{3}{2}\sqrt{9x-9}+24\sqrt{\dfrac{x-1}{64}}=-17\)

Làm mất căn mẫu và thu gọn

1) \(\dfrac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}+\dfrac{5-2\sqrt{5}}{2\sqrt{5}-4}\)

2) \(\left(1-\dfrac{5+\sqrt{5}}{1+\sqrt{5}}\right)\left(\dfrac{5-\sqrt{5}}{1-\sqrt{5}}-1\right)\)

3) \(\left(\dfrac{3\sqrt{125}}{15}-\dfrac{10-4\sqrt{5}}{\sqrt{5}-2}\right)\dfrac{1}{\sqrt{5}}\)

4) \(\dfrac{1}{1+\sqrt{2}}-\dfrac{1}{1-\sqrt{2}}\)

5) \(\dfrac{1}{3+\sqrt{5}}-\dfrac{1}{\sqrt{5}-3}\)

6) \(\dfrac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}+\dfrac{\sqrt{2}-\sqrt{3}}{\sqrt{2}+\sqrt{3}}\)

7) \(\dfrac{4}{1-\sqrt{3}}+\dfrac{\sqrt{3}-1}{\sqrt{3}+1}\)

8) \(\dfrac{\sqrt{2}-1}{\sqrt{2}+1}-\dfrac{3}{\sqrt{2}-1}\)

9) \(\dfrac{\sqrt{2}}{\sqrt{\sqrt{2}+1}-1}-\dfrac{\sqrt{2}}{\sqrt{\sqrt{2}+1}+1}\)

10) \(\dfrac{\sqrt{15}-\sqrt{12}}{\sqrt{5}-2}-\dfrac{1}{2-\sqrt{3}}\)

11) \(\dfrac{5}{1+\sqrt{6}}-\dfrac{3\sqrt{2}-2\sqrt{3}}{\sqrt{3}-\sqrt{2}}\)

12) \(\dfrac{5}{3-\sqrt{7}}-\dfrac{3}{\sqrt{2}+\sqrt{3}}+\dfrac{-1}{\sqrt{2}-1}\)

Giúp em giải với ạ! Help me~!

Tính :

a) \(\dfrac{5+2\sqrt{5}}{\sqrt{5}}+\dfrac{3+\sqrt{3}}{\sqrt{3}}-\left(\sqrt{5}+\sqrt{3}\right)\)

b) \(\left(\dfrac{1}{2-\sqrt{5}}+\dfrac{2}{\sqrt{5}+\sqrt{3}}\right):\dfrac{1}{\sqrt{21+12\sqrt{3}}}\)

c) \(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{4}}{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}\)

d) \(\sqrt{21-6\sqrt{6}}+\sqrt{9+2\sqrt{18}}-2\sqrt{6+3\sqrt{3}}\)

e) \(\sqrt{6+2\sqrt{5-\sqrt{13+\sqrt{48}}}}\)

f) \(\dfrac{\left(5+2\sqrt{6}\right)\left(49-20\sqrt{6}\right)\left(\sqrt{5-2\sqrt{6}}\right)}{9\sqrt{3}-11\sqrt{2}}\)

g) \(\left(\dfrac{1-a\sqrt{a}}{1-\sqrt{a}}+\sqrt{a}\right)-\dfrac{\left(1-\sqrt{a}\right)^2}{\left(1-a\right)^2}\)