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. \(\dfrac{9+4\sqrt{5}}{\sqrt{5}+2}\)
Giải 5 câu sau:
1. \(\dfrac{\sqrt{5}+2}{\sqrt{5}-2}\)
2. \(\dfrac{5\sqrt{2}-2\sqrt{5}}{\sqrt{2}-\sqrt{5}}\)
3. \(\dfrac{\sqrt{20}-3\sqrt{10}}{3-\sqrt{5}}\)
4. \(\dfrac{6-2\sqrt{5}}{3+\sqrt{5}}\)
5. \(\dfrac{9+4\sqrt{5}}{\sqrt{5}+2}\)
Rút gọn :
\(\dfrac{1}{\sqrt{1}-\sqrt{2}}-\dfrac{1}{\sqrt{2}-\sqrt{3}}+\dfrac{1}{\sqrt{3}-\sqrt{4}}-\dfrac{1}{\sqrt{4}-\sqrt{5}}+\dfrac{1}{\sqrt{5}-\sqrt{6}}-\dfrac{1}{\sqrt{6}-\sqrt{7}}+\dfrac{1}{\sqrt{7}-\sqrt{8}}-\dfrac{1}{\sqrt{8}-\sqrt{9}}\)
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) \(\sqrt{8-2\sqrt{15}}-\sqrt{8+2\sqrt{15}}=-2\sqrt{3}\)
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, \(\left(1-\dfrac{5+\sqrt{5}}{1+\sqrt{5}}\right)\left(\dfrac{5-\sqrt{5}}{1-\sqrt{5}}-1\right)\)
1 ) thực hiện phép tính
b) \(4\sqrt{\dfrac{9}{2}}+\sqrt{2}+\sqrt{\dfrac{1}{18}}\)
c) \(4\sqrt{20}-3\sqrt{125}+5\sqrt{45}-15\sqrt{\dfrac{1}{5}}\)
d) \(\dfrac{3}{\sqrt{5}+\sqrt{2}}+\dfrac{1}{\sqrt{2}-1}-\dfrac{4}{3-\sqrt{5}}\)
e) \(\dfrac{\sqrt{7}+7}{\sqrt{7}+1}-\dfrac{\sqrt{7}-\sqrt{14}}{1-\sqrt{2}}+\dfrac{2\sqrt{35}-2\sqrt{7}}{1-\sqrt{5}}\)
3) giải phương trình
a) \(\sqrt{4x-8}+5\sqrt{x-2}-\sqrt{9x-18}=20\)
ai giúp e với ! làm câu nào cũng được hết ạ
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 Đúng hoặc Sai,nếu sai thì sửa lại cho đúng
a/\(\dfrac{5}{2\sqrt{5}}=\dfrac{\sqrt{5}}{2}\) ; b/\(\dfrac{2\sqrt{2}+2}{5\sqrt{2}}=\dfrac{2+\sqrt{2}}{10}\) ; c/\(\dfrac{2}{\sqrt{3}-1}=\sqrt{3}-1\) ; d/\(\dfrac{8}{2\sqrt{8}-1}=\dfrac{P\left(2\sqrt{8}+1\right)}{4P-1}\) ; e/\(\dfrac{1}{\sqrt{x}-\sqrt{y}}=\dfrac{\sqrt{x}+\sqrt{y}}{x-y}\)
2 Rút gọn các biểu thức
a/\(\dfrac{2+\sqrt{2}}{1+\sqrt{2}}\) ; b/\(\dfrac{a-\sqrt{a}}{1-\sqrt{a}}\) ; c/\(\dfrac{3+\sqrt{3}}{3-\sqrt{3}}+\dfrac{3-\sqrt{3}}{3+\sqrt{3}}\) ; d/\(\sqrt{\dfrac{3-\sqrt{5}}{3+\sqrt{5}}+\sqrt{\dfrac{3+\sqrt{5}}{3-\sqrt{5}}}}\)
\(\left(\dfrac{6-2\sqrt{2}}{3-\sqrt{2}}-\dfrac{5}{\sqrt{5}}\right)\) : \(\dfrac{1}{2-\sqrt{5}}\)
Rút gọn biểu thức
\(a.\dfrac{\sqrt{5}-2\sqrt{3}}{\sqrt{5}+\sqrt{3}}-\dfrac{2\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\)
\(b.x\sqrt{2x+2}+\left(x+1\right)\sqrt{\dfrac{2}{x+1}}-4\sqrt{\dfrac{x+1}{2}}\)
