Chương I - Căn bậc hai. Căn bậc ba
Các câu hỏi tương tự
tính
C = \(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
E = ( 4 + \(\sqrt{15}\) )(\(\sqrt{10}-\sqrt{6}\))\(\sqrt{4-\sqrt{15}}\)
K = \(\dfrac{\dfrac{\sqrt{2+\sqrt{3}}}{2}}{\dfrac{\sqrt{2+\sqrt{3}}}{2}-\dfrac{2}{\sqrt{6}}+\dfrac{\sqrt{2+\sqrt{3}}}{2\sqrt{3}}}\)
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, \(\left(\dfrac{3\sqrt{125}}{15}-\dfrac{10-4\sqrt{5}}{\sqrt{5}-2}\right)\cdot\dfrac{1}{\sqrt{5}}\)
a) \(\sqrt{\dfrac{2-\sqrt{3}}{2}}+\dfrac{1-\sqrt{3}}{2}\)
b) \(\sqrt{41+6\sqrt{6}-12\sqrt{10}-4\sqrt{15}}+2\sqrt{5}-\sqrt{3}\)
Tính (rút gọn)
a) left(sqrt{3+sqrt{5}}right)left(sqrt{10}+sqrt{2}right)left(3-sqrt{5}right)
b) left(4+sqrt{15}right)left(sqrt{10-sqrt{6}}right)sqrt{4-}sqrt{15}
c) left(sqrt{6}+sqrt{2}right)left(sqrt{3}-2right)sqrt{sqrt{3+2}}
d) left(2sqrt{4+sqrt{6-2sqrt{5}}}right)left(sqrt{10}-sqrt{2}right)
f)sqrt{dfrac{3-sqrt{5}}{2-sqrt{3}}}
g)dfrac{sqrt{2+sqrt{3}}}{3+sqrt{3}}
h)sqrt{4-sqrt{15}}+sqrt{4+sqrt{15}}-2sqrt{3-sqrt{5}}
Đọc tiếp
Tính (rút gọn)
a) \(\left(\sqrt{3+\sqrt{5}}\right)\left(\sqrt{10}+\sqrt{2}\right)\left(3-\sqrt{5}\right)\)
b) \(\left(4+\sqrt{15}\right)\left(\sqrt{10-\sqrt{6}}\right)\sqrt{4-}\sqrt{15}\)
c) \(\left(\sqrt{6}+\sqrt{2}\right)\left(\sqrt{3}-2\right)\sqrt{\sqrt{3+2}}\)
d) \(\left(2\sqrt{4+\sqrt{6-2\sqrt{5}}}\right)\left(\sqrt{10}-\sqrt{2}\right)\)
f)\(\sqrt{\dfrac{3-\sqrt{5}}{2-\sqrt{3}}}\)
g)\(\dfrac{\sqrt{2+\sqrt{3}}}{3+\sqrt{3}}\)
h)\(\sqrt{4-\sqrt{15}}+\sqrt{4+\sqrt{15}}-2\sqrt{3-\sqrt{5}}\)
rút gọn
\(\dfrac{2\sqrt{15}-2\sqrt{10}+\sqrt{6}-3}{2\sqrt{15}-2\sqrt{10}-\sqrt{3}+\sqrt{6}}\)
Rút gọn:
a) \(\dfrac{\left(5\sqrt{2}+2\sqrt{5}\right)\left(\sqrt{3}-3\sqrt{2}\right)}{\sqrt{30}}\)
b) \(\dfrac{5\sqrt{7}-4\sqrt{35}+7\sqrt{5}}{\sqrt{35}}\)
c) \(\dfrac{6\sqrt{6}-2\sqrt{12}+3-\sqrt{2}}{2\sqrt{6}+1}\)
d) \(\dfrac{10\sqrt{18}+5\sqrt{3}-15\sqrt{27}}{\sqrt{3\left(\sqrt{6}-4\right)}}\)
Rút gọn:
a) \(\dfrac{\left(5\sqrt{2}+2\sqrt{5}\right)\left(\sqrt{3}-3\sqrt{2}\right)}{\sqrt{30}}\)
b) \(\dfrac{5\sqrt{7}-4\sqrt{35}+7\sqrt{5}}{\sqrt{35}}\)
c) \(\dfrac{6\sqrt{6}-2\sqrt{12}+3-\sqrt{2}}{2\sqrt{6}+1}\)
d) \(\dfrac{10\sqrt{18}+5\sqrt{3}-15\sqrt{27}}{\sqrt{3}\left(\sqrt{6}-4\right)}\)
Câu 1: Rút gọn:
a) \(2\sqrt{18}-4\sqrt{50}-3\sqrt{32}\)
b) \(\sqrt{14-6\sqrt{5}}+\sqrt{6+2\sqrt{5}}\)
c) \(\dfrac{\sqrt{10}+10}{1+\sqrt{10}}-\dfrac{5\sqrt{2}-2\sqrt{5}}{\sqrt{5}-\sqrt{2}}\)
Câu 2: Giải phương trình:
\(\sqrt{9x^2-30x+25}=5\)
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) \(\left(\dfrac{\sqrt{5}}{\sqrt{2}+1}+\dfrac{14}{2\sqrt{2}-1}-\dfrac{6}{2-\sqrt{2}}\right).\sqrt{17-12\sqrt{2}}\)