Trục căn thức ở mẫu và rút gọn

a, (\(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6}-2}-\frac{12}{3-\sqrt{6}}\))(\(\sqrt{6} +11\))

b,(\(1-\frac{5+\sqrt{5}}{1+\sqrt{5}}\))(\(\frac{5-\sqrt{5}}{1-\sqrt{5}}-1\))

c,\(\frac{3+2\sqrt{3}}{\sqrt{3}}+\frac{2+\sqrt{2}}{\sqrt{2}+1}\)- (\(\sqrt{2}+\sqrt{3}\))

d,(\(\frac{5-2\sqrt{5}}{2-\sqrt{5}}-2\))(\(\frac{5+3\sqrt{5}}{3+\sqrt{5}}-2\))

Đề bài: Rút gọn các biểu thức:

1. \(\sqrt{343a}\) + \(\sqrt{63a}\) - \(\sqrt{28a}\) với a lớn bằng 0

2. - \(\sqrt{36b}\) - 1/3\(\sqrt{54b}\) + 1/5\(\sqrt{150b}\) với b lớn bằng 0

3. \(\sqrt{9x+6\sqrt{3x-1}}\) - \(\sqrt{\sqrt{9}}\) - \(\sqrt{\sqrt{9x^2-6x+1}}\) với x > bằng 1/3

4. \(\sqrt{\frac{x^2}{5}}\) + \(\sqrt{\frac{x^2}{20}}\) + \(\sqrt{\frac{49x^2}{20}}\) với x < 0

giúp mik vs

trục căn thức ở mẫu

\(\frac{1\sqrt{2}}{\sqrt{2}.\sqrt{2}}\)   \(\frac{1\sqrt[]{3}}{\sqrt{3}.\sqrt{3}}\)\(\frac{2\sqrt{5}-5}{\sqrt{5}-2}\)\(\frac{6-2\sqrt{6}}{2-\sqrt{6}}\)\(\frac{5\sqrt{6}-6\sqrt{5}}{\sqrt{5}-\sqrt{6}}\)\(\frac{1}{\sqrt{5}-1}\)\(\frac{1}{4-2\sqrt{a}+a}\)\(\frac{1}{b-2\sqrt{b}+4}\)\(\frac{1}{b-3\sqrt{b}+9}\)

Rút gọn các biểu thức sau :

a,\(\frac{3}{\sqrt{5}-\sqrt{2}}+\frac{4}{\sqrt{6}+\sqrt{2}}\)

b  \(\left(\sqrt{20}-\sqrt{45}+\sqrt{5}\right).\sqrt{5}\)

c,\(\left(5\sqrt{\frac{1}{5}}+\frac{1}{2}\sqrt{20}-\frac{5}{4}\sqrt{\frac{4}{5}+\sqrt{5}}\right):2\sqrt{5}\)

d \(2\sqrt{3}\left(2\sqrt{6}-\sqrt{3}+1\right)\)

e \(\sqrt{2+\sqrt{3}}\times\sqrt{2-\sqrt{3}}\)

g \(\frac{5\sqrt{7}-7\sqrt{5}+2\sqrt{70}}{\sqrt{35}}\)

h   \(\left(\sqrt{\frac{2}{3}}+\sqrt{\frac{3}{2}}\right)\times\sqrt{6}\)

i \(\left(1+\sqrt{2}+\sqrt{3}\right)\times\left(1+\sqrt{2}-\sqrt{3}\right)\)

k \(\frac{1}{\sqrt{5}+\sqrt{3}}-\frac{1}{\sqrt{5}-\sqrt{3}}\)

l \(\frac{1}{2+\sqrt{3}}+\frac{\sqrt{2}}{\sqrt{6}}-\frac{2}{3+\sqrt{3}}\)

m \(\frac{\sqrt{5+2\sqrt{6}}+\sqrt{8-2\sqrt{15}}}{\sqrt{7+2\sqrt{10}}}\)

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, \(G=\frac{\sqrt{15-10\sqrt{2}}+\sqrt{13+4\sqrt{10}-\sqrt{11-2\sqrt{10}}}}{2\sqrt{3+2\sqrt{2}}+\sqrt{9-4\sqrt{2}+\sqrt{12+8\sqrt{2}}}}\)

rút gọn các biểu thức 

a/ A=\(\sqrt{7+2\sqrt{6}}+\sqrt{7-2\sqrt{6}}-2\sqrt{6}\)

b/ B= \(\sqrt{7+2\sqrt{10}}-\sqrt{7+2\sqrt{10}}-\sqrt{8}\)

c/ C=\(\sqrt{14+4\sqrt{6}}-\sqrt{14-4\sqrt{6}}\)

d/ D=\(\sqrt{3+\sqrt{5}}-\sqrt{3-\sqrt{5}}\)

e/ E=\(\frac{\sqrt{2-\sqrt{3}}}{\sqrt{2}}\)

f/ F=\(\frac{\sqrt{x-\sqrt{2x-1}}}{\sqrt{2}}với\frac{1}{2}\le x< 1\) 

Bài 2: Thực hiện phép tính

a) \(\sqrt{5}-\sqrt{48}+5\sqrt{27}-\sqrt{45}\)

b) \(\left(\sqrt{5}+\sqrt{2}\right)\left(3\sqrt{2}-1\right)\)

c) \(3\sqrt{50}-2\sqrt{75}-4\frac{\sqrt{54}}{\sqrt{3}}-3\sqrt{\frac{1}{3}}\)

d) \(\sqrt{\left(\sqrt{3}-3\right)^2}+\sqrt{4-2\sqrt{3}}\)

e) \(\sqrt{48-2\sqrt{135}}-\sqrt{45}+\sqrt{18}\)

f) \(\frac{5\sqrt{2}-2\sqrt{5}}{\sqrt{5}-\sqrt{2}}+\frac{6}{2-\sqrt{10}}-\frac{20}{\sqrt{10}}\)

Bài 3: Thực hiện phép tính

a) \(\sqrt{9-4\sqrt{5}}\)

b) \(2\sqrt{3}+\sqrt{48}-\sqrt{75}-\sqrt{243}\)

c) \(\sqrt{4+\sqrt{8}}.\sqrt{2+\sqrt{2+\sqrt{2}}}.\sqrt{2-\sqrt{2+\sqrt{2}}}\)

d) \(\sqrt{3+2\sqrt{2}}-\sqrt{6-4\sqrt{2}}\)

e) \(\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}-\frac{\sqrt{5}+1}{\sqrt{5}-1}\)

f*) \(\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)

Bài 4: Rút gọn

a) \(3\sqrt{2x}-5\sqrt{8x}+7\sqrt{18x}\)

b) \(\left(2\sqrt{3}+\sqrt{4}\right)\left(\sqrt{3}-2\right)\)

c) \(\sqrt{3+2\sqrt{2}}+\sqrt{\left(\sqrt{2}-2\right)^2}\)

d) \(\sqrt{4-\sqrt{15}}-\sqrt{4+\sqrt{15}}+\sqrt{6}\)

e) \(\left(\frac{5-\sqrt{5}}{\sqrt{5}}-2\right)\left(\frac{4}{1+\sqrt{5}}+4\right)\)

f) \(\frac{1}{5}\sqrt{50}-2\sqrt{96}-\frac{\sqrt{30}}{\sqrt{15}}+12\sqrt{\frac{1}{6}}\)