\(\dfrac{1}{\sqrt{2}-\sqrt{3}}\times\sqrt{\dfrac{3\sqrt{2}-2\sqrt{3}}{3\sqrt{2}+2\sqrt{3}}}\)
\(=\dfrac{\sqrt{2}+\sqrt{3}}{2-3}\times\sqrt{\dfrac{\left(3\sqrt{2}-2\sqrt{3}\right)^2}{18-12}}\)
\(=-\left(\sqrt{3}+\sqrt{2}\right)\times\dfrac{\sqrt{2}\times\sqrt{3}\times\left(\sqrt{3}-\sqrt{2}\right)}{\sqrt{6}}\)
\(=-\left(3-2\right)\)
= - 1
Rút gọn :
\(\dfrac{\sqrt{3-2\sqrt{2}}}{\sqrt{17-12\sqrt{2}}}-\dfrac{\sqrt{3+2\sqrt{2}}}{\sqrt{17+12\sqrt{2}}}\)
Rút gọn biểu thức
a) \(\dfrac{\sqrt{14-6\sqrt{5}}}{\sqrt{5}-3}\)
b)\(\dfrac{\sqrt{3+\sqrt{5}}}{\sqrt{2}}\)
c)\(\dfrac{2+\sqrt{2}}{\sqrt{1,5+\sqrt{2}}}\)
d) \(\dfrac{\sqrt{20}}{\sqrt{5}}+\dfrac{\sqrt{117}}{\sqrt{13}}+\dfrac{\sqrt{272}}{\sqrt{17}}+\dfrac{\sqrt{105}}{\sqrt{2\dfrac{1}{7}}}\)
e)\(\dfrac{x\sqrt{x}-y\sqrt{y}}{x+\sqrt{xy}+y},x,y>0\)
f)\(\dfrac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
g)\(\sqrt{\dfrac{2+a-2\sqrt{2a}}{a+3-2\sqrt{3a}}}v\text{ới}a>0,a\ne3\)
M = \(\dfrac{x+3}{x-9}+\dfrac{2}{\sqrt{x}+3}-\dfrac{1}{\sqrt{x}-3}\)
a) Rút gọn M
b) Tìm x để M = \(\dfrac{\sqrt{x}+1}{\sqrt{x}+2}\)
2.4 Rút gọn biểu thức
\(a,\dfrac{3-\sqrt{x}}{x-9}\) ( vs x ≥ 0, x≠ 9)
b, \(\dfrac{x-5\sqrt{x}+6}{\sqrt{x}-3}\)( vs x ≥ 0 ; x ≠ 9)
c, \(6-2x-\sqrt{9-6x+x^2}\left(x< 3\right)\)
Rút gọn biểu thức:
h) \(\sqrt{\dfrac{3+\sqrt{5}}{\sqrt{3-\sqrt{5}}}}+\sqrt{\dfrac{3-\sqrt{5}}{\sqrt{3+\sqrt{5}}}}\)
Mong mng giúp ạ
câu1 rút gọn
a)\(\sqrt{4-2\sqrt{3}}-\sqrt{3}\)
b)\(\dfrac{x^2+2\sqrt{2}x+2}{x^2-2}\left(x\ne\sqrt{2},x\ne-\sqrt{2}\right)\)
c)\(\sqrt{9\text{x}^2}-2\text{x}\left(x< 0\right)\)
d)\(\sqrt{11+6\sqrt{2}}-3+\sqrt{2}\)
e)\(\dfrac{x^2-5}{x+\sqrt{5}}\left(x\ne-\sqrt{5}\right)\)
1. \(\left(\dfrac{\sqrt{x}}{\sqrt{x}+2}-\dfrac{4}{x+2\sqrt{x}}\right):\left(1+\dfrac{1}{\sqrt{x}}\right)\)
Rút gọn biểu thức A
tìm a để biểu thức có nghĩa:
a) \(\sqrt{\dfrac{-a}{3}}\)
b) \(-\sqrt{\dfrac{1}{a^2}}\)
c) \(\sqrt{\dfrac{\left(1-a\right)^3}{a^2}}\)
d) \(\sqrt{\dfrac{a^{2^{ }}+1}{1-2a}}\)
e) \(\sqrt{a^2-1}\)
f) \(\sqrt{\dfrac{2a-1}{2-a}}\)
1.Thu gọn
A=\(\dfrac{1}{\sqrt{2}+\sqrt{3}}+\dfrac{1}{\sqrt{3}+\sqrt{4}}+\dfrac{1}{\sqrt{4}+\sqrt{5}}+...+\dfrac{1}{\sqrt{2020}+\sqrt{2021}}\)
