1 bài muốn chết tới 3 bài tớ vào quan tài nằm trước
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1. Rút gọn. a, Bsqrt{2-sqrt{2sqrt{5}-2}}-sqrt{2+sqrt{2sqrt{5}-2}} b,Cfrac{3sqrt{10}+sqrt{20}-3sqrt{6}-sqrt{12}}{sqrt{5}-sqrt{3}} c, Cfrac{sqrt{2}+sqrt{3}+sqrt{6}+sqrt{8}+sqrt{16}}{sqrt{2}+sqrt{3}+sqrt{4}}
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1. Rút gọn. a, B=\(\sqrt{2-\sqrt{2\sqrt{5}-2}}-\sqrt{2+\sqrt{2\sqrt{5}-2}}\) b,C=\(\frac{3\sqrt{10}+\sqrt{20}-3\sqrt{6}-\sqrt{12}}{\sqrt{5}-\sqrt{3}}\) c, C=\(\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
Rút gọn:
a) \(\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+\sqrt{48}}}}\)
b) \(\dfrac{\sqrt{3}-\sqrt{5+\sqrt{24}}+\sqrt{\sqrt{72}+11}}{\sqrt{6+\sqrt{20}}+\sqrt{2}-\sqrt{7+\sqrt{40}}}\)
Tính
a/ A=\(\sqrt{6-2\sqrt{5}}\) - \(\sqrt{5}\)
b/ B=\(\sqrt{17\sqrt{2}-24}\)+ 4
c/ C=\(\sqrt{12+6\sqrt{3}-4}\)- \(\sqrt{3}\)
Rút gọn biểu thứcA frac{sqrt{3}+sqrt{11+6sqrt{2}}-sqrt{5+2sqrt{6}}}{sqrt{2}+sqrt{6+2sqrt{5}}-sqrt{7+2sqrt{10}}}B sqrt{5sqrt{3}+5sqrt{48-10sqrt{7+4sqrt{3}}}}C sqrt{2-sqrt{3}}-sqrt{2+sqrt{3}}D sqrt{28+6sqrt{3}}-sqrt{28-6sqrt{3}}E 6x+sqrt{9x^2-12x+4}F 5x-sqrt{x^2+4x+4}
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Rút gọn biểu thức
A = \(\frac{\sqrt{3}+\sqrt{11+6\sqrt{2}}-\sqrt{5+2\sqrt{6}}}{\sqrt{2}+\sqrt{6+2\sqrt{5}}-\sqrt{7+2\sqrt{10}}}\)
B = \(\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)
C = \(\sqrt{2-\sqrt{3}}-\sqrt{2+\sqrt{3}}\)
D = \(\sqrt{28+6\sqrt{3}}-\sqrt{28-6\sqrt{3}}\)
E = \(6x+\sqrt{9x^2-12x+4}\)
F = \(5x-\sqrt{x^2+4x+4}\)
tính P= a3 +b3- 3(a+b)+2018. Biết
a=\(\sqrt[3]{5+2\sqrt{6}}+\sqrt[3]{5-2\sqrt{6}}\)
\(b=\sqrt[3]{17+12\sqrt{2}}+\sqrt[3]{17-12\sqrt{2}}\)
Tính:a,-0,8.sqrt{left(-0,125right)^2}b,sqrt{left(-2right)^6}+sqrt{left(-3right)^4}c,sqrt{3+2sqrt{2}}-sqrt{2}d,sqrt{9-4sqrt{5}}-sqrt{5}e,sqrt{16-6sqrt{7}}-2sqrt{7}g,sqrt{30+12sqrt{6}}+sqrt{30-12sqrt{16}}
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Tính:
\(a,-0,8.\sqrt{\left(-0,125\right)^2}\)
\(b,\sqrt{\left(-2\right)^6}+\sqrt{\left(-3\right)^4}\)
\(c,\sqrt{3+2\sqrt{2}}-\sqrt{2}\)
\(d,\sqrt{9-4\sqrt{5}}-\sqrt{5}\)
\(e,\sqrt{16-6\sqrt{7}}-2\sqrt{7}\)
\(g,\sqrt{30+12\sqrt{6}}+\sqrt{30-12\sqrt{16}}\)
Rút gọn
1) \(B=\sqrt{\sqrt{7}+6+\sqrt{13-2\sqrt{64-6\sqrt{7}}}}\)
2) \(C=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)
3) \(D=\frac{2\sqrt{3+\sqrt{5-\sqrt{13+\sqrt{48}}}}}{\sqrt{6}+\sqrt{2}}\)
Chứng minh A,B là số nguyên với:
A = \(\sqrt{6-2\sqrt{5}}\)- \(\sqrt{6+2\sqrt{5}}\)
B= \(\frac{\sqrt{3-2\sqrt{2}}}{\sqrt{17}-12\sqrt{2}}-\frac{\sqrt{3+2\sqrt{2}}}{\sqrt{17+12\sqrt{2}}}\)
Tính :a ) Sfrac{1}{sqrt{1}sqrt{3}}+frac{1}{sqrt{3}+sqrt{5}}+frac{1}{sqrt{5}+sqrt{7}}+.....+frac{1}{sqrt{2017}+sqrt{2019}}b ) Sfrac{1}{sqrt{2}+sqrt{4}}+frac{1}{sqrt{4}+sqrt{6}}+....+frac{1}{sqrt{100}+sqrt{102}}c ) Sfrac{1}{sqrt{1}+sqrt{2}}+frac{1}{sqrt{2}+sqrt{3}}+.....+frac{1}{sqrt{100}+sqrt{101}}d ) Sfrac{1}{sqrt{3}+sqrt{6}}+frac{1}{sqrt{6}+sqrt{9}}+frac{1}{sqrt{9}+sqrt{12}}+....+frac{1}{sqrt{2016}+sqrt{2019}}
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Tính :
a ) \(S=\frac{1}{\sqrt{1}\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{7}}+.....+\)\(\frac{1}{\sqrt{2017}+\sqrt{2019}}\)
b ) \(S=\frac{1}{\sqrt{2}+\sqrt{4}}+\frac{1}{\sqrt{4}+\sqrt{6}}+....+\frac{1}{\sqrt{100}+\sqrt{102}}\)
c ) \(S=\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+.....+\frac{1}{\sqrt{100}+\sqrt{101}}\)
d ) \(S=\frac{1}{\sqrt{3}+\sqrt{6}}+\frac{1}{\sqrt{6}+\sqrt{9}}+\frac{1}{\sqrt{9}+\sqrt{12}}+....+\frac{1}{\sqrt{2016}+\sqrt{2019}}\)