\(=\dfrac{\left(\sqrt{3}+2\right)\left(3-2\sqrt{3}+4\right)}{3-2\sqrt{3}+4}+\dfrac{1}{2+\sqrt{3}}\)
\(=\sqrt{3}+2+\dfrac{1}{2+\sqrt{3}}\)
\(=\dfrac{\left(2+\sqrt{3}\right)^2+1}{2+\sqrt{3}}=\dfrac{8+4\sqrt{3}}{2+\sqrt{3}}=4\)
Rút gọn các biểu thức sau:
a. \(\dfrac{8}{\left(\sqrt{5}+\sqrt{3}\right)^2}\) - \(\dfrac{8}{\left(\sqrt{5}-\sqrt{3}\right)^2}\)
b.\(\dfrac{1}{4-3\sqrt{2}}\) - \(\dfrac{1}{4+3\sqrt{2}}\)
c.\(\left(\dfrac{\sqrt{7}+3}{\sqrt{7}-3}-\dfrac{\sqrt{7}-3}{\sqrt{7}+3}\right)\): \(\sqrt{28}\)
d.\(\dfrac{3}{\sqrt{6}-\sqrt{3}}\)+\(\dfrac{4}{\sqrt{7}+\sqrt{3}}\)
\(\dfrac{-2}{\sqrt{3}-1}\) \(\dfrac{\sqrt{5}}{\sqrt{7}-3}\) \(\dfrac{3\sqrt{3}-2}{1-2\sqrt{3}}\) \(\dfrac{14}{\sqrt{10}+\sqrt{3}}\) Trục căn thức ở mẫu:
giúp mik vs
7) (\(\sqrt{\dfrac{3}{2}}\) - \(\sqrt{\dfrac{2}{3}}\)) : \(\dfrac{1}{\sqrt{6}}\)
8) ( 1+ \(\sqrt{2}\) + \(\sqrt{3}\) ) ( 1 + \(\sqrt{2}\) - \(\sqrt{3}\) )
\(\dfrac{\sqrt{3-\sqrt{5}}\left(3+\sqrt{5}\right)}{\sqrt{10}+\sqrt{2}}\)
\(\dfrac{10+2\sqrt{10}}{\sqrt{5}+\sqrt{2}}\)+\(\dfrac{8}{1-\sqrt{5}}\)
\(\dfrac{5+\sqrt{7}}{9-\sqrt{23+8\sqrt{7}}}\)+\(\dfrac{5-\sqrt{7}}{2+\sqrt{16+6\sqrt{7}}}\)
\(\dfrac{1}{\sqrt{2}+\sqrt{2+\sqrt{3}}}\)+\(\dfrac{1}{\sqrt{2}-\sqrt{2+\sqrt{3}}}\)
Chứng minh đẳng thức
\(\left(4-\sqrt{7}\right)^2=23-8\sqrt{7}\)
\(\sqrt{9-4\sqrt{5}}-\sqrt{5}=-2\)
\(\dfrac{\sqrt{4-2\sqrt{3}}}{1+\sqrt{2}}:\dfrac{\sqrt{2}-1}{\sqrt{3}+1}=2\)
\(\left(\dfrac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}-\dfrac{\sqrt{216}}{3}\right).\dfrac{1}{\sqrt{6}}=-1,5\)
Chứng minh đẳng thức
\(\left(4-\sqrt{7}\right)^2=23-8\sqrt{7}\)
\(\sqrt{9-4\sqrt{5}}-\sqrt{5}=-2\)
\(\dfrac{\sqrt{4-2\sqrt{3}}}{1+\sqrt{2}}:\dfrac{\sqrt{2}-1}{\sqrt{3}-1}=2\)
\(\left(\dfrac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}-\dfrac{\sqrt{216}}{3}\right).\dfrac{1}{\sqrt{6}}=-1,5\)
1) rút gọn
A= \(3\sqrt{2}+5\sqrt{8}-2\sqrt{50}\)
B= \(\dfrac{1}{3+\sqrt{5}}+\dfrac{1}{3-\sqrt{5}}\)
C= \(\sqrt{7-4\sqrt{3}}+\sqrt{12+6\sqrt{3}}\)
Giúp mk vs ạ mk cần gấp
\(\left(6\right)\dfrac{3\sqrt{x}}{5\sqrt{x}-1}\le-3\)
\(\left(7\right)\dfrac{8\sqrt{x}+8}{6\sqrt{x}+9}>\dfrac{8}{3}\)
\(\left(8\right)\dfrac{\sqrt{x}-2}{2\sqrt{x}-3}< -4\)
\(\left(9\right)\dfrac{4\sqrt{x}+6}{5\sqrt{x}+7}\le-\dfrac{2}{3}\)
\(\left(10\right)\dfrac{6\sqrt{x}-2}{7\sqrt{x}-1}>-6\)
(1) rút gọn biểu thức:
a) A= \(3\sqrt{2}+5\sqrt{8}-2\sqrt{50}\)
b) B= \(\sqrt{7-4\sqrt{3}}+\sqrt{12+6\sqrt{3}}\)
c) C= \(\dfrac{1}{3+\sqrt{5}}+\dfrac{1}{3-\sqrt{5}}\)
d) D= \(\sqrt[3]{27}-\sqrt[3]{-8}-\sqrt[3]{125}\)
giúp mk vs ạ mai mk hc rồi
bài 1 thực hiện pt
a)\(\sqrt{75}-2\sqrt{27}+\sqrt{48}\)
b)\(\dfrac{\left(12\sqrt{50}-8\sqrt{200}+\dfrac{7}{3}\sqrt{450}\right)}{\sqrt{10}}\)
c)\(\sqrt{8+2\sqrt{7}}-\sqrt{11-4\sqrt{7}}\)giải hộ mik
