Trục căn thức ở mẫu:
a,\(\frac{1}{\sqrt{2}-1}\)

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

c,\(\frac{5}{\sqrt{7}-\sqrt{2}}\)

d,\(\frac{6}{2\sqrt{3}+\sqrt{2}}\)

e,\(\frac{1}{2\sqrt{a}+1}\)

g,\(\frac{2xy}{2\sqrt{x}+3\sqrt{y}}\)

h,\(\frac{x\sqrt{x}-1}{\sqrt{x}-1}\)

i,\(\frac{a-9b}{\sqrt{a}-3\sqrt{b}}\)

k,\(\frac{15-2\sqrt{5}}{3\sqrt{15}-2\sqrt{3}}\)

trục căn thức ở mẫu :

a,\(\frac{3}{\sqrt{5}};\frac{2\sqrt{3}}{\sqrt{2}};\frac{a}{\sqrt{b}};\frac{x+1}{\sqrt{x^2-1}}\)

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

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

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

bài 1) rút gọn

1) 5√\(\frac{1}{5}\) 2)\(\frac{12}{5}\)√\(\frac{5}{4}\) 3)\(\frac{30}{5\sqrt{6}}\) 4) \(\frac{20}{2\sqrt{5}}\) 5)\(\frac{2-\sqrt{2}}{\sqrt{2}}\) 6) \(\frac{11+\sqrt{11}}{1+\sqrt{ }11}\) 7) \(\frac{\sqrt{21-\sqrt{7}}}{1-\sqrt{3}}\) 8)\(\frac{\sqrt{2+\sqrt{3}}}{2+\sqrt{6}}\) 9)\(\frac{\sqrt{10-\sqrt{2}}}{\sqrt{5-}1}\) 10)\(\frac{2\sqrt{3}-3\sqrt{2}}{\sqrt{3}-\sqrt[]{2}}\)

bài 2) với các biểu thức đã cho là có nghĩa và rút gọn

1)\(\frac{x-\sqrt{x}}{\sqrt{x}-1}\) 2)\(\frac{x\sqrt{x}-2x}{2-\sqrt{x}}\) 3) \(\frac{x\sqrt{y}-y\sqrt{x}}{\sqrt{x}-\sqrt{y}}\) 4) \(\frac{a\sqrt{b}-\sqrt{a}}{\sqrt{b}-b\sqrt{a}}\) 5) \(\frac{a-1}{\sqrt{a}+1}\) 6) \(\frac{4-x}{2\sqrt{x}-x}\) 7)\(\frac{a+1+2\sqrt{a}}{1+\sqrt{a}}\) 8)\(\frac{3\sqrt{x}-x}{3+2\sqrt{3x}-x}\) 9)\(\frac{y+12-4\sqrt{3y}}{y-12}\) 10)\(\frac{4\sqrt{x}-x-4}{x-4}\) 11)\(\frac{x+y-2\sqrt{xy}}{x\sqrt{y}-y\sqrt{x}}\)

Trục căn thức ở mẫu

a)\(\frac{\sqrt{3}-\sqrt{2}}{\sqrt{5}}\)         b)\(\frac{2\sqrt{5}}{\sqrt{3}}\)        c)\(\frac{1}{2\sqrt{32}}\)      d)\(\frac{x+\sqrt{y}}{x\sqrt{y}}\)      e)\(\frac{3\sqrt{2}-1}{3-\sqrt{8}}\)      f)\(\frac{3-3\sqrt{2}}{2\sqrt{2}-3\sqrt{6}}\)             g \(\frac{xy}{\sqrt{x}-\sqrt{y}}\)

1. Tính: 

a) A= \(\sqrt{6+2\sqrt{2}.\sqrt{3-\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-\sqrt{128}}}}}\)(dấu căn đầu tiên là của cả biểu thức)

b) B= \(\frac{2}{\sqrt{3}}+\frac{\sqrt{2}}{3}+\frac{2}{\sqrt{3}}.\sqrt{\frac{5}{12}-\frac{1}{\sqrt{6}}}\)

2. Cho:

A= \(\left(\left(\frac{1}{\sqrt{x}}+\frac{1}{\sqrt{y}}\right).\frac{2}{\sqrt{x}+\sqrt{y}}+\frac{1}{x}+\frac{1}{y}\right):\frac{\sqrt{x^3}+y\sqrt{x}+x\sqrt{y}+\sqrt{y^3}}{\sqrt{x^3y}+\sqrt{xy^3}}\)với x>0, y>0

a) Rút gọn A

b) Cho xy=16. Tìm x,y để A có GTNN. Tìm Gt đó

Rút gọn biểu thức

a)\(\sqrt{3}-\sqrt{2}-\sqrt{\sqrt{3}+\sqrt{2}}\)

b)\(\sqrt{11-4\sqrt{7}}-\sqrt{2}\cdot\sqrt{8+3\sqrt{7}}\)

c)\(\frac{x+\sqrt{xy}}{y+\sqrt{xy}}\)

d)\(\frac{\sqrt{x}}{\sqrt{x}-1}-\frac{2\sqrt{x}-1}{x-\sqrt{x}}\left(x>0;x\ne1\right)\)

e)\(\frac{4-4\sqrt{x}}{x-2\sqrt{x}-35}+\frac{2}{\sqrt{x}-7}-\frac{3}{\sqrt{x}+5}\left(x\ge0:x\ne49\right)\)

f)\(\frac{x\sqrt{y}+y\sqrt{x}}{\sqrt{xy}}:\frac{1}{\sqrt{x}-\sqrt{y}}\)