Violympic toán 9
Các câu hỏi tương tự
Đưa biểu thức trong căn về dạng hình phương của một tổng hoặc một hiệu:
a/ sqrt{7-2sqrt{10}}-sqrt{6-2sqrt{5}}
b/ sqrt{33-12sqrt{6}}+sqrt{15-6sqrt{6}}
c/sqrt{9-4sqrt{5}}+sqrt{12-2sqrt{35}}
d/ sqrt{4-2sqrt{3}}+sqrt{28-10sqrt{3}}
e/ frac{sqrt{5}-sqrt{15}}{1-sqrt{3}}-sqrt{21+4sqrt{5}}
Đọc tiếp
Đưa biểu thức trong căn về dạng hình phương của một tổng hoặc một hiệu:
a/ \(\sqrt{7-2\sqrt{10}}-\sqrt{6-2\sqrt{5}}\)
b/ \(\sqrt{33-12\sqrt{6}}+\sqrt{15-6\sqrt{6}}\)
c/\(\sqrt{9-4\sqrt{5}}+\sqrt{12-2\sqrt{35}}\)
d/ \(\sqrt{4-2\sqrt{3}}+\sqrt{28-10\sqrt{3}}\)
e/ \(\frac{\sqrt{5}-\sqrt{15}}{1-\sqrt{3}}-\sqrt{21+4\sqrt{5}}\)
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=\(\frac{3+\sqrt{5}}{\sqrt{2}+\sqrt{3+\sqrt{5}}}+\frac{3-\sqrt{5}}{\sqrt{2}-\sqrt{3-\sqrt{5}}}\)
giúp mk tính
a,sqrt{5}-sqrt{48}+5sqrt{27}-sqrt{45}
b,(sqrt{5}+sqrt{2}) (3sqrt{2}-1)
c,3sqrt{50}-2sqrt{75}-4dfrac{sqrt{54}}{sqrt{3}}-3sqrt{dfrac{1}{3}}
d, sqrt{left(sqrt{3}-3right)^2}+sqrt{4-2sqrt{3}}
e, sqrt{48-2sqrt{135}}-sqrt{45}+sqrt{18}
f, dfrac{5sqrt{2}-2sqrt{5}}{sqrt{5}-sqrt{2}}+dfrac{6}{2-sqrt{10}}-dfrac{20}{sqrt{10}}
bài 2
a, sqrt{9-4sqrt{5}}
b,2sqrt{3}+sqrt{48}-sqrt{75}-sqrt{243}
csqrt{4+sqrt{8}}.sqrt{2+sqrt{2+sqrt{2}}}.sqrt{2-sqrt{2+sqrt{2}}}
d, sqrt{3+2sqrt{2}}-sqrt{6-4sqr...
Đọc tiếp
giúp mk tính
a,\(\sqrt{5}-\sqrt{48}+5\sqrt{27}-\sqrt{45}\)
b,(\(\sqrt{5}+\sqrt{2}\)) (\(3\sqrt{2}-1\))
c,\(3\sqrt{50}-2\sqrt{75}-4\dfrac{\sqrt{54}}{\sqrt{3}}-3\sqrt{\dfrac{1}{3}}\)
d, \(\sqrt{\left(\sqrt{3}-3\right)^2}+\sqrt{4-2\sqrt{3}}\)
e, \(\sqrt{48-2\sqrt{135}}-\sqrt{45}+\sqrt{18}\)
f, \(\dfrac{5\sqrt{2}-2\sqrt{5}}{\sqrt{5}-\sqrt{2}}+\dfrac{6}{2-\sqrt{10}}-\dfrac{20}{\sqrt{10}}\)
bài 2
a, \(\sqrt{9-4\sqrt{5}}\)
b,\(2\sqrt{3}+\sqrt{48}-\sqrt{75}-\sqrt{243}\)
c\(\sqrt{4+\sqrt{8}}.\sqrt{2+\sqrt{2+\sqrt{2}}}.\sqrt{2-\sqrt{2+\sqrt{2}}}\)
d, \(\sqrt{3+2\sqrt{2}}-\sqrt{6-4\sqrt{2}}\)
e,\(\dfrac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}\)+\(\dfrac{\sqrt{3}+\sqrt{5}}{\sqrt{5}-\sqrt{3}}-\dfrac{\sqrt{5}+1}{\sqrt{5}-1}\)
f, \(\sqrt{5\sqrt{3+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)
Trục căn ở mẫu:
\(a)\frac{5}{\sqrt{10}}\\ b)\frac{-2}{1-\sqrt{5}}\\ c)\frac{4}{\sqrt{3}+\sqrt{2}}\\ d)\frac{1}{3-2\sqrt{2}}\\ e)\frac{6-\sqrt{6}}{1-\sqrt{6}}\\ g)\frac{3\sqrt{2}-2\sqrt{3}}{2\left(\sqrt{3}-\sqrt{2}\right)}\\ h)\frac{\sqrt{3}-3}{\sqrt{3}-1}\\ i)\frac{\sqrt{15}}{5\sqrt{3}+3\sqrt{5}}\)
Bài 1: Rút gọn biểu thức
a) Asqrt{26+15sqrt{3}}
b) Bsqrt{4+sqrt{7}}-sqrt{4-sqrt{7}}-sqrt{2}
c) Csqrt{8-2sqrt{15}}-sqrt{8+2sqrt{15}}
d) Dleft(sqrt{6}-2right)left(5+sqrt{24}right)sqrt{5-sqrt{24}}
e) Eleft(sqrt{10}-sqrt{2}right)left(sqrt{3+sqrt{5}}right)
f) Fsqrt{sqrt{5}-sqrt{3-sqrt{29-12sqrt{5}}}}
g) Gleft(2-sqrt{3}right)sqrt{26+15sqrt{3}}-left(2+sqrt{3}right)sqrt{26-15sqrt{3}}
h) Hfrac{left(2+sqrt{3}right)sqrt{2-sqrt{3}}}{sqrt{2+sqrt{3}}}
Đọc tiếp
Bài 1: Rút gọn biểu thức
a) \(A=\sqrt{26+15\sqrt{3}}\)
b) \(B=\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}-\sqrt{2}\)
c) \(C=\sqrt{8-2\sqrt{15}}-\sqrt{8+2\sqrt{15}}\)
d) \(D=\left(\sqrt{6}-2\right)\left(5+\sqrt{24}\right)\sqrt{5-\sqrt{24}}\)
e) \(E=\left(\sqrt{10}-\sqrt{2}\right)\left(\sqrt{3+\sqrt{5}}\right)\)
f) \(F=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
g) \(G=\left(2-\sqrt{3}\right)\sqrt{26+15\sqrt{3}}-\left(2+\sqrt{3}\right)\sqrt{26-15\sqrt{3}}\)
h) \(H=\frac{\left(2+\sqrt{3}\right)\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\)
Rút gọn
Hleft(sqrt{3}-1right)sqrt{6+2sqrt{2}.sqrt{3-sqrt{sqrt{2}+sqrt{12}+sqrt{18-sqrt{128}}}}}
Ffrac{left(5+2sqrt{6}right)left(49-20sqrt{6}right)sqrt{5-2sqrt{6}}}{9sqrt{3}-11sqrt{2}}
Gsqrt{4+sqrt{5sqrt{3}+5sqrt{48-10sqrt{7+4sqrt{3}}}}}
Efrac{2sqrt{3+sqrt{5-13+sqrt{48}}}}{sqrt{6}+sqrt{2}}
Dsqrt{4+sqrt{15}}+sqrt{4-sqrt{15}}-2sqrt{3-sqrt{5}}
Zsqrt{4+sqrt{10+2sqrt{5}}}+sqrt{4-sqrt{10-2sqrt{5}}}
Đọc tiếp
Rút gọn
H=\(\left(\sqrt{3}-1\right)\sqrt{6+2\sqrt{2}.\sqrt{3-\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-\sqrt{128}}}}}\)
F=\(\frac{\left(5+2\sqrt{6}\right)\left(49-20\sqrt{6}\right)\sqrt{5-2\sqrt{6}}}{9\sqrt{3}-11\sqrt{2}}\)
G=\(\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)
E=\(\frac{2\sqrt{3+\sqrt{5-13+\sqrt{48}}}}{\sqrt{6}+\sqrt{2}}\)
D=\(\sqrt{4+\sqrt{15}}+\sqrt{4-\sqrt{15}}-2\sqrt{3-\sqrt{5}}\)
Z=\(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10-2\sqrt{5}}}\)
Trục căn thức ở mẫu
a)\(\dfrac{\sqrt{6}+\sqrt{14}}{2\sqrt{3}-\sqrt{7}}\)
b)\(\dfrac{5\sqrt{5}+3\sqrt{3}}{\sqrt{5}+\sqrt{3}}\)
c)\(\dfrac{3+4\sqrt{3}}{\left(\sqrt{6}+\sqrt{2}\right)-\sqrt{5}}\)
Thực hiện phép tính:
a) sqrt{6+2sqrt{5}}-sqrt{6-2sqrt{5}}
b)sqrt{24-8sqrt{5}}+sqrt{9+4sqrt{5}}
c)sqrt{6-4sqrt{2}}+sqrt{22-12sqrt{2}}
d)sqrt{41+12sqrt{5}}-sqrt{46-6sqrt{5}}
e)sqrt{7+4sqrt{3}}-sqrt{7-4sqrt{3}}
f)sqrt{17-12sqrt{2}}+sqrt{9+4sqrt{2}}
g)sqrt{43+24sqrt{3}}-sqrt{49-sqrt{8sqrt{3}}}
h)sqrt{53-20sqrt{7}}-sqrt{64+6sqrt{7}}
Đọc tiếp
Thực hiện phép tính:
a) \(\sqrt{6+2\sqrt{5}}-\sqrt{6-2\sqrt{5}}\)
b)\(\sqrt{24-8\sqrt{5}}+\sqrt{9+4\sqrt{5}}\)
c)\(\sqrt{6-4\sqrt{2}}+\sqrt{22-12\sqrt{2}}\)
d)\(\sqrt{41+12\sqrt{5}}-\sqrt{46-6\sqrt{5}}\)
e)\(\sqrt{7+4\sqrt{3}}-\sqrt{7-4\sqrt{3}}\)
f)\(\sqrt{17-12\sqrt{2}}+\sqrt{9+4\sqrt{2}}\)
g)\(\sqrt{43+24\sqrt{3}}-\sqrt{49-\sqrt{8\sqrt{3}}}\)
h)\(\sqrt{53-20\sqrt{7}}-\sqrt{64+6\sqrt{7}}\)
So sánh 2 số: \(R=\dfrac{3+\sqrt{5}}{2\sqrt{2}+\sqrt{3+\sqrt{5}}}+\dfrac{3-\sqrt{5}}{2\sqrt{2}-\sqrt{3-\sqrt{5}}}\)
\(S=\dfrac{4+\sqrt{7}}{3\sqrt{2}+\sqrt{4+\sqrt{7}}}+\dfrac{4-\sqrt{7}}{3\sqrt{2}-\sqrt{4-\sqrt{7}}}\)