\(\left(\dfrac{6-2\sqrt{2}}{3-\sqrt{2}}-\dfrac{5}{\sqrt{5}}\right):\left(\dfrac{1}{2-\sqrt{5}}\right)\\ =\left(\dfrac{2\left(3-\sqrt{2}\right)}{3-\sqrt{2}}-\dfrac{\sqrt{5^2}}{\sqrt{5}}\right).\left(2-\sqrt{5}\right)\\ =\left(2-\sqrt{5}\right).\left(2-\sqrt{5}\right)\\ =\left(2-\sqrt{5}\right)^2\\ =2^2-2.2\sqrt{5}+\sqrt{5^2}\\ =9-4\sqrt{5}\)
Trục căn thức và thực hiện phép tính:
a, \(\left(\dfrac{15}{\sqrt{6}+1}+\dfrac{4}{\sqrt{6}-2}-\dfrac{12}{3-\sqrt{6}}\right)\left(\sqrt{6}-11\right)\)
b, \(\left(1-\dfrac{5+\sqrt{5}}{1+\sqrt{5}}\right)\left(\dfrac{5-\sqrt{5}}{1-\sqrt{5}}-1\right)\)
B1: thực hiện phép tính
a )\(\dfrac{\sqrt{6}-\sqrt{15}}{\sqrt{35}-\sqrt{14}}\)
b ) \(\dfrac{10+2\sqrt{10}}{\sqrt{5}+\sqrt{2}}+\dfrac{8}{1-\sqrt{5}}\)
c )\(\dfrac{\sqrt{3-\sqrt{5}.}\left(3+\sqrt{5}\right)}{\sqrt{10}+\sqrt{2}}\)
d ) \(\dfrac{1}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{1}{\sqrt{2}-\sqrt{2+\sqrt{3}}}\)
B2:chúng minh vế phải bằng vế trái
a) \(\dfrac{21+8\sqrt{5}}{4+\sqrt{5}}.\sqrt{9-4\sqrt{5}}=\sqrt{5}-2\)
b) \(\sqrt{8-2\sqrt{15}}-\sqrt{8+2\sqrt{15}}=-2\sqrt{3}\)
Rút gọn các biểu thức :
a) \(\dfrac{2}{\sqrt{3}-1}-\dfrac{2}{\sqrt{3}+1}\)
b) \(\dfrac{5}{12\left(2\sqrt{5}+3\sqrt{2}\right)}-\dfrac{5}{12\left(2\sqrt{5}-3\sqrt{2}\right)}\)
c) \(\dfrac{5+\sqrt{5}}{5-\sqrt{5}}+\dfrac{5-\sqrt{5}}{5+\sqrt{5}}\)
d) \(\dfrac{\sqrt{3}}{\sqrt{\sqrt{3+1}}-1}-\dfrac{\sqrt{3}}{\sqrt{\sqrt{3+1}}+1}\)
Rút gọn biểu thức
\(a.\dfrac{\sqrt{5}-2\sqrt{3}}{\sqrt{5}+\sqrt{3}}-\dfrac{2\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\)
\(b.x\sqrt{2x+2}+\left(x+1\right)\sqrt{\dfrac{2}{x+1}}-4\sqrt{\dfrac{x+1}{2}}\)
Bài 1 Rút gọn biểu thức:
a) \(\dfrac{\sqrt{3-\sqrt{5}.}\left(3+\sqrt{5}\right)}{\sqrt{10}+\sqrt{2}}\)
b) \(\dfrac{4}{\sqrt{3}+1}+\dfrac{1}{\sqrt{3}-1}+\dfrac{6}{\sqrt{3}-3}\)
1. \(\dfrac{-2}{\sqrt{3}-1}\)
2. \(\dfrac{5}{1-\sqrt{6}}\)
3. \(\dfrac{2+\sqrt{5}}{2-\sqrt{5}}\)
4. \(\dfrac{1}{5+2\sqrt{6}}\)
5. \(\dfrac{\sqrt{5}+2}{\sqrt{5}-2}\)
6. \(\dfrac{5\sqrt{2}-2\sqrt{5}}{\sqrt{2}-\sqrt{5}}\)
7. \(\dfrac{\sqrt{20}-3\sqrt{10}}{3-\sqrt{2}}\)
8. \(\dfrac{6-2\sqrt{5}}{3+\sqrt{5}}\)
9. \(\dfrac{9+4\sqrt{5}}{\sqrt{5}+2}\)
Bài 1)Rút gọn:
A=\(5\sqrt{4x}-3\sqrt{\dfrac{100x}{9}}-\dfrac{4}{3}\sqrt{\dfrac{x^3}{4}}\left(x>0\right)\)
B=\(\left(\dfrac{5-2\sqrt{5}}{2-\sqrt{5}}-2\right)\)\(\left(\dfrac{5+3\sqrt{5}}{3+\sqrt{5}}-2\right)\)
-giúp mình với ạ-
Cho M= \(\left(1-\dfrac{x-3\sqrt{x}}{x-9}\right):\left(\dfrac{9-x}{x+\sqrt{x}-6}-\dfrac{\sqrt{x}-3}{2-\sqrt{x}}-\dfrac{\sqrt{x}-2}{\sqrt{x}+3}\right)\)
a) Rút gọn M
b) Tìm các giá trị của x để có \(\dfrac{5}{3}M\) = \(\sqrt{x}+4\)
Bài 1) Rút gọn:
A=5\(\sqrt{4x}-3\sqrt{\dfrac{100x}{9}}-\dfrac{4}{3}\sqrt{\dfrac{x^3}{4}}\) (x>0)
B=\(\left(\dfrac{5-2\sqrt{5}}{2-\sqrt{5}}-2\right)\) \(\left(\dfrac{5+3\sqrt{5}}{3+\sqrt{5}}-2\right)\)
-GIÚP MÌNH VỚI Ạ-
