Violympic toán 9
Các câu hỏi tương tự
I : Rút gọn
\(A=\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+...+\frac{1}{2019\sqrt{2020}+2020\sqrt{2019}}\)
help me !!!
Trục căn ở mẫu:
\(a)\frac{5}{\sqrt{10}}\\ b)\frac{-2}{1-\sqrt{5}}\\ c)\frac{4}{\sqrt{3}+\sqrt{2}}\\ d)\frac{1}{3-2\sqrt{2}}\\ e)\frac{6-\sqrt{6}}{1-\sqrt{6}}\\ g)\frac{3\sqrt{2}-2\sqrt{3}}{2\left(\sqrt{3}-\sqrt{2}\right)}\\ h)\frac{\sqrt{3}-3}{\sqrt{3}-1}\\ i)\frac{\sqrt{15}}{5\sqrt{3}+3\sqrt{5}}\)
Tính
Afrac{3}{sqrt{3}}+frac{2sqrt{3}}{sqrt{3}+1} Bfrac{sqrt{15}-sqrt{12}}{sqrt{5}-2}-frac{1}{2-sqrt{3}}
Cfrac{5+2sqrt{5}}{sqrt{5}}+frac{3+sqrt{3}}{sqrt{3}}-left(sqrt{5}+sqrt{3}right)
Dsqrt{frac{4}{left(2-sqrt{5}right)^2}}-sqrt{frac{4}{left(2+sqrt{5}right)^2}} Efrac{sqrt{10}-sqrt{2}}{sqrt{5}-1}-frac{2-sqrt{2}}{sqrt{2}-1}
Đọc tiếp
Tính
\(A=\frac{3}{\sqrt{3}}+\frac{2\sqrt{3}}{\sqrt{3}+1}\) \(B=\frac{\sqrt{15}-\sqrt{12}}{\sqrt{5}-2}-\frac{1}{2-\sqrt{3}}\)
\(C=\frac{5+2\sqrt{5}}{\sqrt{5}}+\frac{3+\sqrt{3}}{\sqrt{3}}-\left(\sqrt{5}+\sqrt{3}\right)\)
\(D=\sqrt{\frac{4}{\left(2-\sqrt{5}\right)^2}}-\sqrt{\frac{4}{\left(2+\sqrt{5}\right)^2}}\) \(E=\frac{\sqrt{10}-\sqrt{2}}{\sqrt{5}-1}-\frac{2-\sqrt{2}}{\sqrt{2}-1}\)
Rút gọn
a, frac{2sqrt{3-1}}{sqrt{15}}-frac{2-sqrt{5}}{sqrt{3}}-frac{4sqrt{15}-10sqrt{3}}{15}
b, left(sqrt{a}-frac{1}{sqrt{a}}right)left(frac{sqrt{a}+1}{sqrt{a-1}}+frac{sqrt{a-1}}{sqrt{a}+1}right)
c, sqrt{4+sqrt{7}-sqrt{4-sqrt{7}}}
d, 6+2sqrt{2}.3-sqrt{4+sqrt{2sqrt{3}}}
e, sqrt{5}-sqrt{3-sqrt{29-12sqrt{5}}}
Help me !!!
Đọc tiếp
Rút gọn
a, \(\frac{2\sqrt{3-1}}{\sqrt{15}}-\frac{2-\sqrt{5}}{\sqrt{3}}-\frac{4\sqrt{15}-10\sqrt{3}}{15}\)
b, \(\left(\sqrt{a}-\frac{1}{\sqrt{a}}\right)\left(\frac{\sqrt{a}+1}{\sqrt{a-1}}+\frac{\sqrt{a-1}}{\sqrt{a}+1}\right)\)
c, \(\sqrt{4+\sqrt{7}-\sqrt{4-\sqrt{7}}}\)
d, \(6+2\sqrt{2}.3-\sqrt{4+\sqrt{2\sqrt{3}}}\)
e, \(\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}\)
Help me !!!
tinh
a. sqrt{5}-sqrt{48}+5sqrt{27}-sqrt{45}
b.left(sqrt{5}+sqrt{2}right)left(3sqrt{2}-1right)
c.3sqrt{50}-2sqrt{75}-4frac{sqrt{54}}{sqrt{3}}-3sqrt{frac{1}{3}}
d.sqrt{left(sqrt{3}-3right)^2}+sqrt{4-2sqrt{3}}
e.frac{5sqrt{2}-2sqrt{5}}{sqrt{5}-sqrt{2}}+frac{6}{2-sqrt{10}}-frac{20}{sqrt{10}}
f.frac{sqrt{5}-sqrt{3}}{sqrt{5}+sqrt{3}}+frac{sqrt{5}+sqrt{3}}{sqrt{5}-sqrt{3}}-frac{sqrt{5}+1}{sqrt{5}-1}
Đọc tiếp
tinh
a. \(\sqrt{5}-\sqrt{48}+5\sqrt{27}-\sqrt{45}\)
b.\(\left(\sqrt{5}+\sqrt{2}\right)\left(3\sqrt{2}-1\right)\)
c.\(3\sqrt{50}-2\sqrt{75}-4\frac{\sqrt{54}}{\sqrt{3}}-3\sqrt{\frac{1}{3}}\)
d.\(\sqrt{\left(\sqrt{3}-3\right)^2}+\sqrt{4-2\sqrt{3}}\)
e.\(\frac{5\sqrt{2}-2\sqrt{5}}{\sqrt{5}-\sqrt{2}}+\frac{6}{2-\sqrt{10}}-\frac{20}{\sqrt{10}}\)
f.\(\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}-\frac{\sqrt{5}+1}{\sqrt{5}-1}\)
A)\(\frac{6+2\sqrt{5}}{3-\sqrt{5}}-\frac{5+3\sqrt{5}}{\sqrt{5}}+\frac{\sqrt{5}}{2-\sqrt{5}}\)
B)\(\frac{8+2\sqrt{2}}{3-\sqrt{2}}-\frac{2+3\sqrt{2}}{\sqrt{2}}-\frac{3}{\sqrt{2}-1}\)
C)\(\frac{3+\sqrt{2}}{3-\sqrt{3}}-\frac{3+\sqrt{3}}{\sqrt{3}}-\frac{2}{\sqrt{3}-1}\)
D
mọi người giúp em bài này với,em đang cần gấp ạ
bài 2:rút gọn các biểu thức sau
a)Asqrt{5-sqrt{21}}+sqrt{5+sqrt{21}}
b)Bfrac{sqrt{15}-sqrt{5}}{sqrt{3}-1}+frac{5-2sqrt{5}}{2sqrt{5}-4}
c)Cleft(1+frac{11-sqrt{11}}{1-sqrt{11}}right)left(frac{11+sqrt{11}}{1+sqrt{11}}+1right)
d)Dfrac{sqrt{2}}{sqrt{2}-sqrt{3}}-frac{sqrt{2}}{sqrt{2}+sqrt{3}}
e)Efrac{1}{sqrt{2}-sqrt{3}}sqrt{frac{3sqrt{2}-2sqrt{3}}{3sqrt{2}+2sqrt{3}}}
Đọc tiếp
mọi người giúp em bài này với,em đang cần gấp ạ
bài 2:rút gọn các biểu thức sau
a)A=\(\sqrt{5-\sqrt{21}}+\sqrt{5+\sqrt{21}}\)
b)B=\(\frac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}+\frac{5-2\sqrt{5}}{2\sqrt{5}-4}\)
c)C=\(\left(1+\frac{11-\sqrt{11}}{1-\sqrt{11}}\right)\left(\frac{11+\sqrt{11}}{1+\sqrt{11}}+1\right)\)
d)D=\(\frac{\sqrt{2}}{\sqrt{2}-\sqrt{3}}-\frac{\sqrt{2}}{\sqrt{2}+\sqrt{3}}\)
e)E=\(\frac{1}{\sqrt{2}-\sqrt{3}}\sqrt{\frac{3\sqrt{2}-2\sqrt{3}}{3\sqrt{2}+2\sqrt{3}}}\)
a. P (3+sqrt{2}+sqrt{6})(sqrt{6-3sqrt{3}})
b. A(frac{15}{sqrt{6}+1}+frac{4}{sqrt{6}-2}-frac{12}{3-sqrt{6}}): (sqrt{6}+11)
c. B frac{sqrt{8-2sqrt{12}}}{sqrt{3}-1}-sqrt{8}
d. C sqrt{4+sqrt{7}}-sqrt{4-sqrt{7}}-sqrt{2}
đ. Dfrac{1}{sqrt{2}-sqrt{3}}sqrt{frac{3sqrt{2}-2sqrt{3}}{3sqrt{2}+2sqrt{3}}}
e. E sqrt{8+2sqrt{10+2sqrt{5}}}+sqrt{8-2sqrt{10+2sqrt{5}}}
ê. G sqrt{4+5sqrt{3}+5sqrt{48-10sqrt{7+4sqrt{3}}}}
g. Hfrac{2sqrt{4+sqrt{5+21+sqrt{80}}}}{sqrt{10}-sqrt{2}}
i. Isqrt{frac{4-sqrt{7}}{4+sqrt{7...
Đọc tiếp
a. P= (\(3+\sqrt{2}+\sqrt{6}\))(\(\sqrt{6-3\sqrt{3}}\))
b. A=(\(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6}-2}-\frac{12}{3-\sqrt{6}}\)): (\(\sqrt{6}+11\))
c. B= \(\frac{\sqrt{8-2\sqrt{12}}}{\sqrt{3}-1}\)-\(\sqrt{8}\)
d. C= \(\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}-\sqrt{2}\)
đ. D=\(\frac{1}{\sqrt{2}-\sqrt{3}}\sqrt{\frac{3\sqrt{2}-2\sqrt{3}}{3\sqrt{2}+2\sqrt{3}}}\)
e. E= \(\sqrt{8+2\sqrt{10+2\sqrt{5}}}+\sqrt{8-2\sqrt{10+2\sqrt{5}}}\)
ê. G= \(\sqrt{4+5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)
g. H=\(\frac{2\sqrt{4+\sqrt{5+21+\sqrt{80}}}}{\sqrt{10}-\sqrt{2}}\)
i. I=\(\sqrt{\frac{4-\sqrt{7}}{4+\sqrt{7}}}+\sqrt{\frac{4+\sqrt{7}}{4-\sqrt{7}}}\)
k. K=\(\frac{3+\sqrt{5}}{\sqrt{2}+\sqrt{3+\sqrt{5}}}+\frac{3-\sqrt{5}}{\sqrt{2}-\sqrt{3-\sqrt{5}}}\)
3. a.sqrt{left(4-sqrt{17}right)^2}
b.frac{2sqrt{3}}{2}
c frac{sqrt{6}+sqrt{14}}{text{2√3+√28}}
d.frac{x+1}{sqrt{x^2-1}}
e.frac{x^2-5}{x+sqrt{5}}
f.frac{2}{2-sqrt{3}}
g.frac{sqrt{2}+1}{sqrt{2}-1}
f.frac{xsqrt{x}-1}{sqrt{x}-1}
i.frac{3}{sqrt{20}}+frac{1}{sqrt{60}}-2sqrt{frac{1}{15}}
k.frac{3}{sqrt{5}-sqrt{2}}+frac{4}{sqrt{6}+sqrt{2}}
i.(frac{1}{sqrt{5}-sqrt{3}}+frac{1}{sqrt{5}+sqrt{3}})sqrt{5}
h.left(sqrt{20}-sqrt{45}+sqrt{5}right)sqrt{5}
l.left(5sqrt{3}+3sqrt{5}right):sqrt{15}
m.frac...
Đọc tiếp
3. a.\(\sqrt{\left(4-\sqrt{17}\right)^2}\)
b.\(\frac{2\sqrt{3}}{2}\)
c \(\frac{\sqrt{6}+\sqrt{14}}{\text{2√3+√28}}\)
d.\(\frac{x+1}{\sqrt{x^2-1}}\)
e.\(\frac{x^2-5}{x+\sqrt{5}}\)
f.\(\frac{2}{2-\sqrt{3}}\)
g.\(\frac{\sqrt{2}+1}{\sqrt{2}-1}\)
f.\(\frac{x\sqrt{x}-1}{\sqrt{x}-1}\)
i.\(\frac{3}{\sqrt{20}}+\frac{1}{\sqrt{60}}-2\sqrt{\frac{1}{15}}\)
k.\(\frac{3}{\sqrt{5}-\sqrt{2}}+\frac{4}{\sqrt{6}+\sqrt{2}}\)
i.(\(\frac{1}{\sqrt{5}-\sqrt{3}}+\frac{1}{\sqrt{5}+\sqrt{3}}\))\(\sqrt{5}\)
h.\(\left(\sqrt{20}-\sqrt{45}+\sqrt{5}\right)\sqrt{5}\)
l.\(\left(5\sqrt{3}+3\sqrt{5}\right):\sqrt{15}\)
m.\(\frac{1}{3}\sqrt{48}+3\sqrt{75}-\sqrt{27}-10\sqrt{\frac{4}{3}}\)
n.\(\left(5\sqrt{\frac{1}{5}}+\frac{1}{2}\sqrt{20}-\frac{5}{4}\sqrt{\frac{4}{5}+\sqrt{5}}\right):2\sqrt{5}\)
d\(\left(2+\sqrt{5}\right)^2-\left(2+\sqrt{5}\right)^2\)