Chương I - Căn bậc hai. Căn bậc ba
Các câu hỏi tương tự
Tính B=\(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10-2\sqrt{5}}}\)
C= \(\sqrt{5\sqrt{9}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)
D= \(\sqrt{x+2\sqrt{2x+4}}+\sqrt{x-2\sqrt{2x-4}}\)
# Các bạn giúp mình với ạ :<<
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:
\(\sqrt{9x^2-30x+25}=5\)
Bài 1: Tính
1, Aleft(1-frac{5+sqrt{5}}{1+sqrt{5}}right).left(frac{5-sqrt{5}}{1-sqrt{5}}-1right)
2, Bleft(frac{3sqrt{125}}{15}-frac{10-4sqrt{6}}{sqrt{5}-2}right).frac{1}{sqrt{5}}
3, Cleft(frac{sqrt{1000}}{100}-frac{5sqrt{2}-2sqrt{5}}{2sqrt{5}-8}right).frac{sqrt{10}}{10}
4, Dfrac{1}{sqrt{49+20sqrt{6}}}-frac{1}{sqrt{49-20sqrt{6}}}+frac{1}{sqrt{7-4sqrt{3}}}
5, Efrac{1}{sqrt{4-2sqrt{3}}}-frac{1}{sqrt{7-sqrt{48}}}+frac{3}{sqrt{14-6sqrt{5}}}
6, Ffrac{1}{sqrt{2}-sqrt{3}}sqrt{frac{3sqrt{2}-2sqrt{3}...
Đọc tiếp
Bài 1: Tính
1, \(A=\left(1-\frac{5+\sqrt{5}}{1+\sqrt{5}}\right).\left(\frac{5-\sqrt{5}}{1-\sqrt{5}}-1\right)\)
2, \(B=\left(\frac{3\sqrt{125}}{15}-\frac{10-4\sqrt{6}}{\sqrt{5}-2}\right).\frac{1}{\sqrt{5}}\)
3, \(C=\left(\frac{\sqrt{1000}}{100}-\frac{5\sqrt{2}-2\sqrt{5}}{2\sqrt{5}-8}\right).\frac{\sqrt{10}}{10}\)
4, \(D=\frac{1}{\sqrt{49+20\sqrt{6}}}-\frac{1}{\sqrt{49-20\sqrt{6}}}+\frac{1}{\sqrt{7-4\sqrt{3}}}\)
5, \(E=\frac{1}{\sqrt{4-2\sqrt{3}}}-\frac{1}{\sqrt{7-\sqrt{48}}}+\frac{3}{\sqrt{14-6\sqrt{5}}}\)
6, \(F=\frac{1}{\sqrt{2}-\sqrt{3}}\sqrt{\frac{3\sqrt{2}-2\sqrt{3}}{3\sqrt{2}+2\sqrt{3}}}\)
7, \(G=\frac{\sqrt{15-10\sqrt{2}}+\sqrt{13+4\sqrt{10}-\sqrt{11-2\sqrt{10}}}}{2\sqrt{3+2\sqrt{2}}+\sqrt{9-4\sqrt{2}+\sqrt{12+8\sqrt{2}}}}\)
Bài 1: Rút gọn
a)sqrt{4+sqrt{10+2sqrt{5}}}+sqrt{4-sqrt{10+2sqrt{5}}} ,
b)sqrt{4+sqrt{15}}+sqrt{4-sqrt{15}}-2sqrt{3-sqrt{5}}
c)Asqrt{4+sqrt{5sqrt{3}+5sqrt{48-10sqrt{7+4sqrt{3}}}}}
d)Bsqrt{6+2sqrt{2}sqrt{3-sqrt{sqrt{2}+sqrt{12}+sqrt{18-8sqrt{2}}}}}
e)Csqrt{sqrt{5}-sqrt{3-sqrt{29-12sqrt{5}}}}
f)D dfrac{left(5+4sqrt{6}right)left(49-20sqrt{6}right)left(5-2sqrt{6}right)sqrt{5-2sqrt{6}}}{9sqrt{3}-11sqrt{2}}
Đọc tiếp
Bài 1: Rút gọn
a)\(\sqrt{4+\sqrt{10+2\sqrt{5}}}\)+\(\sqrt{4-\sqrt{10+2\sqrt{5}}}\) ,
b)\(\sqrt{4+\sqrt{15}}\)+\(\sqrt{4-\sqrt{15}}\)-\(2\sqrt{3-\sqrt{5}}\)
c)A=\(\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)
d)B=\(\sqrt{6+2\sqrt{2}\sqrt{3-\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-8\sqrt{2}}}}}\)
e)C=\(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
f)D= \(\dfrac{\left(5+4\sqrt{6}\right)\left(49-20\sqrt{6}\right)\left(5-2\sqrt{6}\right)\sqrt{5-2\sqrt{6}}}{9\sqrt{3}-11\sqrt{2}}\)
Bài 1: Tìm ĐKXĐ
1, sqrt{2x-1}+ frac{sqrt{x-3}}{sqrt{5-x}}
2, sqrt{x-1}+ frac{sqrt{2-x}}{sqrt{x+1}}
Bài 2: Tính
1, A sqrt{6+2sqrt{5}} - sqrt{6-2sqrt{5}}
2, B sqrt{4+sqrt{15}} + sqrt{4-sqrt{15}} - 2sqrt{3-sqrt{5}}
3, C sqrt{4+sqrt{10}+2sqrt{5}} + sqrt{4-sqrt{10}+2sqrt{5}}
4, D sqrt{15-6sqrt{6}} + sqrt{15+6sqrt{6}}
5, E frac{sqrt{2}+sqrt{3}+sqrt{6}+sqrt{8}+4}{sqrt{2}+sqrt{3}+sqrt{4}}
6, F sqrt{left(1-sqrt{2021}right)}. sqrt{2022+2sqrt{2021}}
7, G frac{2+sqrt{3}}{sqrt{2}+sqrt{2+sqr...
Đọc tiếp
Bài 1: Tìm ĐKXĐ
1, \(\sqrt{2x-1}\)+ \(\frac{\sqrt{x-3}}{\sqrt{5-x}}\)
2, \(\sqrt{x-1}\)+ \(\frac{\sqrt{2-x}}{\sqrt{x+1}}\)
Bài 2: Tính
1, A = \(\sqrt{6+2\sqrt{5}}\) - \(\sqrt{6-2\sqrt{5}}\)
2, B = \(\sqrt{4+\sqrt{15}}\) + \(\sqrt{4-\sqrt{15}}\) - \(2\sqrt{3-\sqrt{5}}\)
3, C = \(\sqrt{4+\sqrt{10}+2\sqrt{5}}\) + \(\sqrt{4-\sqrt{10}+2\sqrt{5}}\)
4, D = \(\sqrt{15-6\sqrt{6}}\) + \(\sqrt{15+6\sqrt{6}}\)
5, E = \(\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
6, F = \(\sqrt{\left(1-\sqrt{2021}\right)}\). \(\sqrt{2022+2\sqrt{2021}}\)
7, G = \(\frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}\) + \(\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
Bài 1: Rút gọn
a)sqrt{4+sqrt{10+2sqrt{5}}}+sqrt{4-sqrt{10+2sqrt{5}}} ,
b)sqrt{4+sqrt{15}}+sqrt{4-sqrt{15}}-2sqrt{3-sqrt{5}}
c)Asqrt{4+sqrt{5sqrt{3}+5sqrt{48-10sqrt{7+4sqrt{3}}}}}
d)Bsqrt{6+2sqrt{2}sqrt{3-sqrt{sqrt{2}+sqrt{12}+sqrt{18-8sqrt{2}}}}}
e)Csqrt{sqrt{5}-sqrt{3-sqrt{29-12sqrt{5}}}}
f)Ddfrac{left(5+2sqrt{6}right)left(49-20sqrt{6}right)left(5-2sqrt{6}right)sqrt{5-2sqrt{6}}}{9sqrt{3}-11sqrt{2}}
Mình sửa lại để m.n dễ nhìn hơn!
Đọc tiếp
Bài 1: Rút gọn
a)\(\sqrt{4+\sqrt{10+2\sqrt{5}}}\)+\(\sqrt{4-\sqrt{10+2\sqrt{5}}}\) ,
b)\(\sqrt{4+\sqrt{15}}\)+\(\sqrt{4-\sqrt{15}}\)-\(2\sqrt{3-\sqrt{5}}\)
c)A=\(\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)
d)B=\(\sqrt{6+2\sqrt{2}\sqrt{3-\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-8\sqrt{2}}}}}\)
e)C=\(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
f)D=\(\dfrac{\left(5+2\sqrt{6}\right)\left(49-20\sqrt{6}\right)\left(5-2\sqrt{6}\right)\sqrt{5-2\sqrt{6}}}{9\sqrt{3}-11\sqrt{2}}\)
Mình sửa lại để m.n dễ nhìn hơn!
Rút gọn biểu thức:
a) dfrac{sqrt{9-2sqrt{6}}-sqrt{6}}{sqrt{3}} b)dfrac{5+sqrt{5}}{5-sqrt{5}}+dfrac{5-sqrt{5}}{5+sqrt{5}}
c) sqrt{13+30sqrt{2+sqrt{9+4sqrt{2}}}} d) sqrt{8+2sqrt{10+2sqrt{5}}}+sqrt{8-2sqrt{10+2sqrt{5}}}
e) dfrac{2sqrt{3+sqrt{5-sqrt{13+sqrt{48}}}}}{sqrt{6}-sqrt{2}} f) sqrt{9-sqrt{5sqrt{3}+5sqrt{8+10sqrt{7-4sqrt{3}}}}}
Đọc tiếp
Rút gọn biểu thức:
a) \(\dfrac{\sqrt{9-2\sqrt{6}}-\sqrt{6}}{\sqrt{3}}\) b)\(\dfrac{5+\sqrt{5}}{5-\sqrt{5}}+\dfrac{5-\sqrt{5}}{5+\sqrt{5}}\)
c) \(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\) d) \(\sqrt{8+2\sqrt{10+2\sqrt{5}}}+\sqrt{8-2\sqrt{10+2\sqrt{5}}}\)
e) \(\dfrac{2\sqrt{3+\sqrt{5-\sqrt{13+\sqrt{48}}}}}{\sqrt{6}-\sqrt{2}}\) f) \(\sqrt{9-\sqrt{5\sqrt{3}+5\sqrt{8+10\sqrt{7-4\sqrt{3}}}}}\)
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 = \(\dfrac{\dfrac{\sqrt{2+\sqrt{3}}}{2}}{\dfrac{\sqrt{2+\sqrt{3}}}{2}-\dfrac{2}{\sqrt{6}}+\dfrac{\sqrt{2+\sqrt{3}}}{2\sqrt{3}}}\)
Tính (Rút gọn):
a) \(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
b)\(\sqrt{10+2\sqrt{6}+2\sqrt{10}+2\sqrt{15}}\)
c)\(\left(\sqrt{5+2\sqrt{9\sqrt{5}-19}}-\sqrt{7-\sqrt{5}}\right):2\sqrt{\sqrt{5}-2}\)
d)\(\frac{\sqrt{9+\sqrt{5}}+\sqrt{9-\sqrt{5}}}{\sqrt{9+2\sqrt{19}}}-\sqrt{3-2\sqrt{2}}\)