`(2\sqrt{5} - \sqrt{15})/(\sqrt{5}) = (2\sqrt{5} - \sqrt{3} . \sqrt{5})/(\sqrt{5}) =2 - \sqrt{3}`
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Chương I - Căn bậc hai. Căn bậc ba
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LL
6 tháng 7 2021 lúc 20:39
* Chứng minh đẳng thức
\(\dfrac{2\sqrt{3-\sqrt{5}}\left(3+\sqrt{5}\right)}{\sqrt{10}-\sqrt{2}}-\dfrac{\sqrt{15}+\sqrt{5}}{\sqrt{12}+\sqrt{2}}=\dfrac{3}{2}\)
LL
29 tháng 6 2021 lúc 9:04
* Rút gọn biểu thức
c.\(\dfrac{1}{2\sqrt{2}}-\dfrac{3}{2}\sqrt{4,5}+\dfrac{2}{5}\sqrt{50}\)
d.\(\dfrac{4}{3+\sqrt{5}}-\dfrac{8}{1+\sqrt{5}}+\dfrac{15}{\sqrt{5}}\)
LL
5 tháng 7 2021 lúc 16:31
* Chứng minh đẳng thức
B= \(\dfrac{2\sqrt{3-\sqrt{5}}\left(3+\sqrt{5}\right)}{\sqrt{10}-\sqrt{2}}-\dfrac{\sqrt{15}+\sqrt{5}}{\sqrt{12}+2}=\dfrac{3}{2}\)
LL
7 tháng 7 2021 lúc 12:29
* Chứng minh đẳng thức
\(\dfrac{2\sqrt{3-\sqrt{5}}\left(3+\sqrt{5}\right)}{\sqrt{10}-\sqrt{2}}-\dfrac{\sqrt{15}+\sqrt{5}}{\sqrt{12}+2}=\dfrac{3}{2}\)
Tính
\(A=\sqrt{20}-3\sqrt{8}+5\sqrt{45}\)
\(B=\dfrac{30}{\sqrt{7}-1}+\dfrac{15}{\sqrt{7}+2}\)
\(C=\left(3-\dfrac{5-\sqrt{5}}{\sqrt{5}-1}\right)\left(3+\dfrac{5+\sqrt{5}}{\sqrt{5}+1}\right)\)
\(D=\sqrt{\left(3-\sqrt{2}\right)^2}-\sqrt{\left(1-\sqrt{2}\right)^2}\)
\(E=\sqrt{7-4\sqrt{3}}-\sqrt{3+2\sqrt{3}}\)
1, dfrac{6-sqrt{6}}{sqrt{6}-1}+dfrac{6+sqrt{6}}{sqrt{6}}
2, dfrac{6-6sqrt{3}}{1-sqrt{3}}+dfrac{3sqrt{3}+3}{sqrt{3}+1}
3, dfrac{3+sqrt{3}}{sqrt{3}}+dfrac{sqrt{6}-sqrt{3}}{1-sqrt{2}}
4, dfrac{sqrt{15}-sqrt{12}}{sqrt{5}-2}+dfrac{6+2sqrt{6}}{sqrt{3}+sqrt{2}}
5, left(dfrac{3sqrt{125}}{15}-dfrac{10-4sqrt{5}}{sqrt{5}-2}right)cdotdfrac{1}{sqrt{5}}
Đọc tiếp
1, \(\dfrac{6-\sqrt{6}}{\sqrt{6}-1}+\dfrac{6+\sqrt{6}}{\sqrt{6}}\)
2, \(\dfrac{6-6\sqrt{3}}{1-\sqrt{3}}+\dfrac{3\sqrt{3}+3}{\sqrt{3}+1}\)
3, \(\dfrac{3+\sqrt{3}}{\sqrt{3}}+\dfrac{\sqrt{6}-\sqrt{3}}{1-\sqrt{2}}\)
4, \(\dfrac{\sqrt{15}-\sqrt{12}}{\sqrt{5}-2}+\dfrac{6+2\sqrt{6}}{\sqrt{3}+\sqrt{2}}\)
5, \(\left(\dfrac{3\sqrt{125}}{15}-\dfrac{10-4\sqrt{5}}{\sqrt{5}-2}\right)\cdot\dfrac{1}{\sqrt{5}}\)
Bài: thực hiện phép tính
a. \(\dfrac{12}{1+\sqrt[]{5}}+\dfrac{15}{\sqrt[]{5}}-\dfrac{\sqrt[]{20}-5}{2-\sqrt[]{5}}\)
b. \(\dfrac{2\sqrt[]{x}}{\sqrt[]{x}-1}-\dfrac{3x}{x-\sqrt[]{x}}+\dfrac{1}{\sqrt[]{x}}\left(x>0,x\ne1\right)\)
Tính
a) 3sqrt{2x}-5sqrt{8x}+7sqrt{18x}
b) left(2sqrt{3}+4right)left(sqrt{3}-2right)
c) sqrt{3+2sqrt{2}}+sqrt{left(sqrt{2}-2right)^2}
d) sqrt{4-sqrt{15}}-sqrt{4+sqrt{15}}+sqrt{6}
e) left(dfrac{5-sqrt{5}}{sqrt{5}}-2right)left(dfrac{4}{1+sqrt{5}}+4right)
f) dfrac{1}{5}sqrt{50}-2sqrt{96}-dfrac{sqrt{30}}{sqrt{15}}+12sqrt{dfrac{1}{6}}
Đọc tiếp
Tính
a) \(3\sqrt{2x}-5\sqrt{8x}+7\sqrt{18x}\)
b) \(\left(2\sqrt{3}+4\right)\left(\sqrt{3}-2\right)\)
c) \(\sqrt{3+2\sqrt{2}}+\sqrt{\left(\sqrt{2}-2\right)^2}\)
d) \(\sqrt{4-\sqrt{15}}-\sqrt{4+\sqrt{15}}+\sqrt{6}\)
e) \(\left(\dfrac{5-\sqrt{5}}{\sqrt{5}}-2\right)\left(\dfrac{4}{1+\sqrt{5}}+4\right)\)
f) \(\dfrac{1}{5}\sqrt{50}-2\sqrt{96}-\dfrac{\sqrt{30}}{\sqrt{15}}+12\sqrt{\dfrac{1}{6}}\)
rút gọn :
a)left(dfrac{sqrt{15}-sqrt{5}}{1-sqrt{3}}+dfrac{sqrt{14}-sqrt{7}}{1-sqrt{2}}right):dfrac{1}{sqrt{7}-sqrt{5}}
b) sqrt{dfrac{3sqrt{3}-4}{2sqrt{3}+1}}+sqrt{dfrac{sqrt{3}+4}{5-2sqrt{3}}}
c) dfrac{2sqrt{5}-5sqrt{2}}{sqrt{2}-sqrt{5}}+dfrac{6}{2-sqrt{10}}+sqrt{67+12sqrt{7}}
d) left(dfrac{sqrt{5}}{sqrt{2}+1}+dfrac{14}{2sqrt{2}-1}-dfrac{6}{2-sqrt{2}}right).sqrt{17-12sqrt{2}}
Đọc tiếp
rút gọn :
a)\(\left(\dfrac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}+\dfrac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}\right):\dfrac{1}{\sqrt{7}-\sqrt{5}}\)
b) \(\sqrt{\dfrac{3\sqrt{3}-4}{2\sqrt{3}+1}}+\sqrt{\dfrac{\sqrt{3}+4}{5-2\sqrt{3}}}\)
c) \(\dfrac{2\sqrt{5}-5\sqrt{2}}{\sqrt{2}-\sqrt{5}}+\dfrac{6}{2-\sqrt{10}}+\sqrt{67+12\sqrt{7}}\)
d) \(\left(\dfrac{\sqrt{5}}{\sqrt{2}+1}+\dfrac{14}{2\sqrt{2}-1}-\dfrac{6}{2-\sqrt{2}}\right).\sqrt{17-12\sqrt{2}}\)
rút gọn biểu thức
a.\(2\sqrt{80}+3\sqrt{45}-\sqrt{245}\)
b.\(\dfrac{3}{2+\sqrt{3}}+\dfrac{13}{4-\sqrt{3}}+\dfrac{6}{\sqrt{3}}\)
c.\(\left(\dfrac{\sqrt{14}-\sqrt{7}}{\sqrt{2}-1}+\dfrac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}\right):\dfrac{1}{\sqrt{7}-\sqrt{5}}\)
d.\(\sqrt{\left(2+\sqrt{3}\right)^2}-\sqrt{28-10\sqrt{3}}\)