\(\sqrt{2\sqrt{6}+2\sqrt{3}+6+2\sqrt{2}}-\sqrt{5+2\sqrt{6}}=\sqrt{3+2+1+2\sqrt{3}.\sqrt{2}+2\sqrt{2}+2\sqrt{3}}-\sqrt{3+2\sqrt{2}.\sqrt{3}+2}=\sqrt{3}+\sqrt{2}+1-\sqrt{3}-\sqrt{2}=1\)
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. \(\dfrac{9+4\sqrt{5}}{\sqrt{5}+2}\)
chứng minh :a) 11+6\(\sqrt{2}\)= (3+\(\sqrt{2}\))\(^2\)
b) \(\sqrt{11+6\sqrt{2}}+\sqrt{11-6\sqrt{2}}\)=6
c) \(\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}\)= -2
d) \(\sqrt{49-12\sqrt{5}}-\sqrt{49+12\sqrt{5}}\)=-4
Rút gọn:
a, A = \(\frac{1}{\sqrt{3}+\sqrt{1}}+\frac{1}{\sqrt{5}+\sqrt{3}}+\frac{1}{\sqrt{7}+\sqrt{5}}+\frac{1}{\sqrt{9}+\sqrt{7}}\)
b, B = \(2\sqrt{40\sqrt{12}}-2\sqrt{\sqrt{75}}-3\sqrt{5\sqrt{48}}\)
c, C = \(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6}-2}-\frac{12}{3-\sqrt{6}}-\sqrt{6}\)
d, D = \(\sqrt{x+2\sqrt{2x-4}}+\sqrt{x-2\sqrt{2x-4}}\) với x ≥ 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 biểu thức :
1/ \(\frac{6-6\sqrt{3}}{1-\sqrt{3}}+\frac{3\sqrt{3}+3}{\sqrt{3}+1}\)
2/ \(\frac{\sqrt{6}-\sqrt{3}}{1-\sqrt{2}}+\frac{3+\sqrt{3}}{\sqrt{3}}\)
3/ \(\frac{2-\sqrt{2}}{1-\sqrt{2}}+\frac{\sqrt{2}-\sqrt{6}}{\sqrt{3}-1}\)
\(\sqrt{14-6\sqrt{5}}\)
\(\sqrt{28-12\sqrt{5}}\)
\(\sqrt{7-3\sqrt{5}}\)
\(\left(3-\sqrt{2}\right)\sqrt{11+6\sqrt{2}}\)
\(\sqrt{11-6\sqrt{2}+\sqrt{3-2\sqrt{2}}}\)
giải hộ mình với ạ, làm chi tiết 1 tí ạ
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) \(\sqrt{8-2\sqrt{15}}-\sqrt{8+2\sqrt{15}}=-2\sqrt{3}\)
Rút gọn
1, \(2\sqrt{5}-\sqrt{125}-\sqrt{80}\)
2, \(3\sqrt{2}-\sqrt{8}+\sqrt{50}-4\sqrt{32}\)
3, \(\sqrt{18}-3\sqrt{80}-2\sqrt{50}+2\sqrt{45}\)
4, \(\sqrt{27}-2\sqrt{3}+2\sqrt{48}-3\sqrt{75}\)
5, \(3\sqrt{2}-4\sqrt{18}+\sqrt{32}-\sqrt{50}\)
6, \(2\sqrt{3}-\sqrt{75}+2\sqrt{12}-\sqrt{147}\)
7, \(\sqrt{20}-2\sqrt{45}-3\sqrt{80}+\sqrt{125}\)
8, \(6\sqrt{12}-\sqrt{20}-2\sqrt{27}+\sqrt{125}\)
9, \(4\sqrt{24}-2\sqrt{54}+3\sqrt{6}-\sqrt{150}\)
10, \(2\sqrt{18}-3\sqrt{80}-5\sqrt{147}+5\sqrt{245}-3\sqrt{98}\)
Các bạn ơi !! giúp mik với đi !!!!!
