\(y=\left(\frac{2}{\sqrt{3}-1}-\frac{52}{3\sqrt{3}-1}+\frac{12}{3-\sqrt{3}}\right)\left(5+\sqrt{27}\right)\)
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rút gọn \(a=\left(\frac{2}{\sqrt{3}-1}-\frac{52}{3\sqrt{3}-1}+\frac{12}{3-\sqrt{3}}\right)\left(5+\sqrt{27}\right)\)
B=\(\left(\frac{3}{\sqrt{3}-1}-\frac{52}{3\sqrt{3}-1}+\frac{12}{3-\sqrt{3}}\right)\left(5+\sqrt{27}\right)\)
Lời giải:
\(B=\left(\frac{3}{\sqrt{3}-1}-\frac{52}{3\sqrt{3}-1}+\frac{4\sqrt{3}}{\sqrt{3}-1}\right)(5+3\sqrt{3})\)
\(=\frac{3(3+\sqrt{3}+1)-52+4\sqrt{3}(3+\sqrt{3}+1)}{3\sqrt{3}-1}(5+3\sqrt{3})\)
\(=\frac{-28+19\sqrt{3}}{3\sqrt{3}-1}(5+3\sqrt{3})\)
Biểu thức rút gọn xấu. Mình nghĩ bạn nên xem lại đề.
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Bài 1: Rút gọn biểu thức1) sqrt{12}-sqrt{27}+sqrt{48} 2) left(sqrt{25}+sqrt{20}-sqrt{80}right):sqrt{5}3) 2sqrt{27}-sqrt{frac{16}{3}}-sqrt{48}-sqrt{8frac{1}{3}} 4) frac{1}{sqrt{5}-sqrt{3}}-frac{1}{sqrt{5}+sqrt{3}}5) left(sqrt{125}-sqrt{12}-2sqrt{5}right)left(3sqrt{5}-sqrt{3}+sqrt{27}right) 6) left(3sqrt{20}-sqrt{125}-15sqrt{frac{1}{5}}right).sqrt{5}7) left(6sqrt{128}-frac{3}{5}sqrt{50}+7sqrt{8}right):3sqrt{2} 8) left(2sqrt{48}-frac{3}{2}sqrt{frac{4}{3}}+sqrt{27}right).2sqrt{3...
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Bài 1: Rút gọn biểu thức
1) \(\sqrt{12}-\sqrt{27}+\sqrt{48}\) 2) \(\left(\sqrt{25}+\sqrt{20}-\sqrt{80}\right):\sqrt{5}\)
3) \(2\sqrt{27}-\sqrt{\frac{16}{3}}-\sqrt{48}-\sqrt{8\frac{1}{3}}\) 4) \(\frac{1}{\sqrt{5}-\sqrt{3}}-\frac{1}{\sqrt{5}+\sqrt{3}}\)
5) \(\left(\sqrt{125}-\sqrt{12}-2\sqrt{5}\right)\left(3\sqrt{5}-\sqrt{3}+\sqrt{27}\right)\) 6) \(\left(3\sqrt{20}-\sqrt{125}-15\sqrt{\frac{1}{5}}\right).\sqrt{5}\)
7) \(\left(6\sqrt{128}-\frac{3}{5}\sqrt{50}+7\sqrt{8}\right):3\sqrt{2}\) 8) \(\left(2\sqrt{48}-\frac{3}{2}\sqrt{\frac{4}{3}}+\sqrt{27}\right).2\sqrt{3}\)
9) \(\sqrt{\left(3-2\sqrt{2}\right)^2}-\sqrt{\left(\sqrt{8}-4\right)^2}\) 10) \(\sqrt{\left(4-\sqrt{15}\right)^2}+\sqrt{\left(\sqrt{15}-3\right)^2}\)
11) \(\frac{\sqrt{10}-\sqrt{2}}{\sqrt{5}-1}+\frac{2-\sqrt{2}}{\sqrt{2}-1}\) 12) \(\left(1-\frac{5+\sqrt{5}}{1+\sqrt{5}}\right)\left(\frac{5-\sqrt{5}}{1-\sqrt{5}}-1\right)\)
13) \(\sqrt{15-6\sqrt{6}}\) 14) \(\sqrt{8-2\sqrt{15}}\) 15) \(\sqrt[3]{-2}.\sqrt[3]{32}+\sqrt{2}.\sqrt{32}\)
Bài 7 Thực hiện phép tính a ( frac{sqrt{9}}{2}+frac{sqrt{1}}{2}-sqrt{2} ) sqrt{2}b) left(frac{sqrt{8}}{3}-sqrt{24}+frac{sqrt{50}}{3}right)sqrt{6}c) left(sqrt{6}+sqrt{2}right).left(sqrt{3}-sqrt{2}right)d) left(3sqrt{2}+1right)left(3sqrt{2}-1right)e ) (left(sqrt{5}-2sqrt{3}right)left(sqrt{5}+2sqrt{3}right)g)left(frac{sqrt{2}}{3}-sqrt{frac{3}{2}}right)^2h) sqrt{52}:sqrt{117}i) sqrt{2}:sqrt{72}l ) left(frac{sqrt{1}}{5}-frac{sqrt{9}}{5}right)+sqrt{5}k) left(sqrt{12}+sqrt{27}-sqrt{3}right):sqrt{3}m) ...
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Bài 7 Thực hiện phép tính
a ( \(\frac{\sqrt{9}}{2}+\frac{\sqrt{1}}{2}-\sqrt{2}\) ) \(\sqrt{2}\)
b) \(\left(\frac{\sqrt{8}}{3}-\sqrt{24}+\frac{\sqrt{50}}{3}\right)\sqrt{6}\)
c) \(\left(\sqrt{6}+\sqrt{2}\right).\left(\sqrt{3}-\sqrt{2}\right)\)
d) \(\left(3\sqrt{2}+1\right)\left(3\sqrt{2}-1\right)\)
e ) (\(\left(\sqrt{5}-2\sqrt{3}\right)\left(\sqrt{5}+2\sqrt{3}\right)\)
g)\(\left(\frac{\sqrt{2}}{3}-\sqrt{\frac{3}{2}}\right)^2\)
h) \(\sqrt{52}:\sqrt{117}\)
i) \(\sqrt{2}:\sqrt{72}\)
l ) \(\left(\frac{\sqrt{1}}{5}-\frac{\sqrt{9}}{5}\right)+\sqrt{5}\)
k) \(\left(\sqrt{12}+\sqrt{27}-\sqrt{3}\right):\sqrt{3}\)
m) \(\frac{\sqrt{2}+\sqrt{3}}{\sqrt{3}}\)
n) \(\frac{\sqrt{6-2\sqrt{5}}}{1-\sqrt{5}}\)
a) 2√2 -2
b) -12-√12
c) 3√6 -6
d) 17
e) -7
g) (29-6√12)/18
h) 2/3
l) (-2+5√5)/5
i) 1/6
k) 4
m) (√6+3)/3
n) 1
Thực hiện luôn ra bấm máy tính bố mày chả bấm được?
Tinh
a,sqrt{75}-sqrt{5frac{1}{3}}+frac{9}{2}sqrt{2frac{2}{3}}+2sqrt{27}
b,sqrt{48}+sqrt{5frac{1}{3}}+2sqrt{75}-5sqrt{1frac{1}{3}}
c,left(sqrt{15}+2sqrt{3}right)^2+12sqrt{5}
d,left(sqrt{6}+2right)left(sqrt{3}-sqrt{2}right)
e,left(sqrt{3}+1right)^2-2sqrt{3}+4
f,frac{1}{7+4sqrt{3}}+frac{1}{7-4sqrt{3}}
g,left(frac{1}{sqrt{5}-sqrt{2}}-frac{1}{sqrt{5}+sqrt{2}}+1right)frac{1}{left(sqrt{2}+1right)^2}
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Tinh
\(a,\sqrt{75}-\sqrt{5\frac{1}{3}}+\frac{9}{2}\sqrt{2\frac{2}{3}}+2\sqrt{27}\)
\(b,\sqrt{48}+\sqrt{5\frac{1}{3}}+2\sqrt{75}-5\sqrt{1\frac{1}{3}}\)
\(c,\left(\sqrt{15}+2\sqrt{3}\right)^2+12\sqrt{5}\)
\(d,\left(\sqrt{6}+2\right)\left(\sqrt{3}-\sqrt{2}\right)\)
\(e,\left(\sqrt{3}+1\right)^2-2\sqrt{3}+4\)
\(f,\frac{1}{7+4\sqrt{3}}+\frac{1}{7-4\sqrt{3}}\)
\(g,\left(\frac{1}{\sqrt{5}-\sqrt{2}}-\frac{1}{\sqrt{5}+\sqrt{2}}+1\right)\frac{1}{\left(\sqrt{2}+1\right)^2}\)
a)\(\sqrt{75}-\sqrt{5\frac{1}{3}}+\frac{9}{2}\sqrt{2\frac{2}{3}}+2\sqrt{27}=5\sqrt{3}-\frac{\sqrt{15}}{3}+3\sqrt{3}+6\sqrt{3}=14\sqrt{3}-\frac{\sqrt{15}}{3}\)
b) \(\sqrt{48}+\sqrt{5\frac{1}{3}}+2\sqrt{75}-5\sqrt{1\frac{1}{3}}=4\sqrt{3}+\frac{\sqrt{15}}{3}+10\sqrt{3}-\frac{5\sqrt{3}}{3}=\frac{12\sqrt{3}+30\sqrt{3}-5\sqrt{3}}{3}+\frac{\sqrt{15}}{3}=\frac{37\sqrt{3}+\sqrt{15}}{3}\)
c) \(\left(\sqrt{15}+2\sqrt{3}\right)^2+12\sqrt{5}=\left[\left(\sqrt{15}\right)^2+4\sqrt{45}+\left(2\sqrt{3}\right)^2\right]+12\sqrt{5}=15+12\sqrt{5}+12+12\sqrt{5}=27+24\sqrt{5}\)
d) \(\left(\sqrt{6}+2\right)\left(\sqrt{3}-\sqrt{2}\right)=\sqrt{18}-\sqrt{12}+\sqrt{6}-2\sqrt{2}=3\sqrt{2}-2\sqrt{3}+\sqrt{6}-2\sqrt{2}=\sqrt{2}-2\sqrt{3}+\sqrt{6}\)
e) \(\left(\sqrt{3}+1\right)^2-2\sqrt{3}+4=\left(\sqrt{3}\right)^2+2\sqrt{3}+1-2\sqrt{3}+4=3+2\sqrt{3}+1-2\sqrt{3}+4=8\)
f) \(\frac{1}{7+4\sqrt{3}}+\frac{1}{7-4\sqrt{3}}=\frac{7-4\sqrt{3}+7+4\sqrt{3}}{\left(7+4\sqrt{3}\right)\left(7-4\sqrt{3}\right)}=\frac{14}{1}=14\)
g) \(\left(\frac{1}{\sqrt{5}-\sqrt{2}}-\frac{1}{\sqrt{5}+\sqrt{2}}+1\right)\frac{1}{\left(\sqrt{2}+1\right)^2}=\left(\frac{\sqrt{5}+2-\sqrt{5}+2+5-2}{\left(\sqrt{5}-\sqrt{2}\right)\left(\sqrt{5}+\sqrt{2}\right)}\right)\frac{1}{3+2\sqrt{2}}=\frac{7}{3}.\frac{1}{3+2\sqrt{2}}=\frac{7}{9+6\sqrt{2}}\)
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Rút Gọna,sqrt{75}-sqrt{5frac{1}{3}}+frac{9}{2}sqrt{2frac{2}{3}}+2sqrt{27}b,sqrt{48}+sqrt{5frac{1}{3}}+2sqrt{75}-5sqrt{1frac{1}{3}}c,left(sqrt{12}+2sqrt{27}right)frac{sqrt{3}}{2}-sqrt{150}d,left(sqrt{18}+sqrt{0,5}-3sqrt{frac{1}{3}}right)-left(sqrt{frac{1}{8}-sqrt{75}}right)e,6sqrt{frac{8}{9}}-5sqrt{frac{32}{25}}+14sqrt{frac{18}{49}}f,2sqrt{frac{16}{3}}-3sqrt{frac{1}{27}}-6sqrt{frac{4}{75}}g,left(2sqrt{frac{16}{3}}-3sqrt{frac{1}{27}}-6sqrt{frac{4}{75}}right)sqrt{3}h,left(6sqrt{frac{8}{9}}-5sqrt{fr...
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Rút Gọn
a,\(\sqrt{75}-\sqrt{5\frac{1}{3}}+\frac{9}{2}\sqrt{2\frac{2}{3}}+2\sqrt{27}\)
b,\(\sqrt{48}+\sqrt{5\frac{1}{3}}+2\sqrt{75}-5\sqrt{1\frac{1}{3}}\)
c,\(\left(\sqrt{12}+2\sqrt{27}\right)\frac{\sqrt{3}}{2}-\sqrt{150}\)
d,\(\left(\sqrt{18}+\sqrt{0,5}-3\sqrt{\frac{1}{3}}\right)-\left(\sqrt{\frac{1}{8}-\sqrt{75}}\right)\)
e,\(6\sqrt{\frac{8}{9}}-5\sqrt{\frac{32}{25}}+14\sqrt{\frac{18}{49}}\)
f,\(2\sqrt{\frac{16}{3}}-3\sqrt{\frac{1}{27}}-6\sqrt{\frac{4}{75}}\)
g,\(\left(2\sqrt{\frac{16}{3}}-3\sqrt{\frac{1}{27}}-6\sqrt{\frac{4}{75}}\right)\sqrt{3}\)
h,\(\left(6\sqrt{\frac{8}{9}}-5\sqrt{\frac{32}{25}}+14\sqrt{\frac{18}{49}}\right)\sqrt{\frac{1}{2}}\)
i,\(\frac{1}{2}\sqrt{48}-2\sqrt{75}-\frac{\sqrt{33}}{\sqrt{11}}+5\sqrt{1\frac{1}{3}}\)
j,\(\left(\sqrt{\frac{1}{7}}-\sqrt{\frac{16}{7}}+7\right):\sqrt{7}\)
Tính
\(a,\sqrt{75}-\sqrt{5\frac{1}{3}}+\frac{9}{2}\sqrt{2\frac{2}{3}}+2\sqrt{27}\)
\(b,\sqrt{48}+\sqrt{5\frac{1}{3}}+2\sqrt{75}-5\sqrt{1\frac{1}{3}}\)
\(c,\left(\sqrt{15}+2\sqrt{3}\right)^2+12\sqrt{5}\)
\(d,\left(\sqrt{6}+2\right)\left(\sqrt{3}-\sqrt{2}\right)\)
\(e,\left(\sqrt{3}+1\right)^2-2\sqrt{3}+4\)
frac{3+2sqrt{3}}{sqrt{3}}+frac{2+sqrt{2}}{sqrt{2}+1}-left(sqrt{2}+3right)
0.1cdotsqrt{left(-3right)^2}cdotleft[6sqrt{left(frac{1}{3}right)^2}-sqrt{left(sqrt{3}-2right)^2}right]^2
left(frac{3sqrt{2}+sqrt{6}}{sqrt{12}+2}-frac{sqrt{54}}{3}right)cdotfrac{2}{sqrt{6}}
left(frac{3+2sqrt{3}}{sqrt{3}+2}+frac{2+sqrt{2}}{sqrt{2}+1}right)divleft(1divfrac{1}{sqrt{2}+sqrt{3}}right)
sqrt{frac{5+2sqrt{6}}{5-2sqrt{6}}}+sqrt{frac{5-2sqrt{6}}{5+2sqrt{6}}}
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\(\frac{3+2\sqrt{3}}{\sqrt{3}}+\frac{2+\sqrt{2}}{\sqrt{2}+1}-\left(\sqrt{2}+3\right)\)
\(0.1\cdot\sqrt{\left(-3\right)^2}\cdot\left[6\sqrt{\left(\frac{1}{3}\right)^2}-\sqrt{\left(\sqrt{3}-2\right)^2}\right]^2\)
\(\left(\frac{3\sqrt{2}+\sqrt{6}}{\sqrt{12}+2}-\frac{\sqrt{54}}{3}\right)\cdot\frac{2}{\sqrt{6}}\)
\(\left(\frac{3+2\sqrt{3}}{\sqrt{3}+2}+\frac{2+\sqrt{2}}{\sqrt{2}+1}\right)\div\left(1\div\frac{1}{\sqrt{2}+\sqrt{3}}\right)\)
\(\sqrt{\frac{5+2\sqrt{6}}{5-2\sqrt{6}}}+\sqrt{\frac{5-2\sqrt{6}}{5+2\sqrt{6}}}\)
1) frac{3+2sqrt{3}}{sqrt{3}}+frac{2+sqrt{2}}{sqrt{2}+1}-left(sqrt{2}+3right)2) 0.1sqrt{left(-3right)^2}cdotleft[6sqrt{left(-frac{1}{3}right)^2}-sqrt{left(sqrt{3}-2right)^2}right]^23) left(frac{3+2sqrt{3}}{sqrt{3}+2}+frac{2+sqrt{2}}{sqrt{2}+1}right)divleft(1divfrac{1}{sqrt{2}+sqrt{3}}right)4) left(frac{3sqrt{2}+sqrt{6}}{sqrt{12}+2}-frac{sqrt{54}}{3}right)cdotfrac{2}{sqrt{6}}5) sqrt{frac{5+2sqrt{6}}{5-2sqrt{6}}}+sqrt{frac{5-2sqrt{6}}{5+2sqrt{6}}}
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1) \(\frac{3+2\sqrt{3}}{\sqrt{3}}+\frac{2+\sqrt{2}}{\sqrt{2}+1}-\left(\sqrt{2}+3\right)\)
2) \(0.1\sqrt{\left(-3\right)^2}\cdot\left[6\sqrt{\left(-\frac{1}{3}\right)^2}-\sqrt{\left(\sqrt{3}-2\right)^2}\right]^2\)
3) \(\left(\frac{3+2\sqrt{3}}{\sqrt{3}+2}+\frac{2+\sqrt{2}}{\sqrt{2}+1}\right)\div\left(1\div\frac{1}{\sqrt{2}+\sqrt{3}}\right)\)
4) \(\left(\frac{3\sqrt{2}+\sqrt{6}}{\sqrt{12}+2}-\frac{\sqrt{54}}{3}\right)\cdot\frac{2}{\sqrt{6}}\)
5) \(\sqrt{\frac{5+2\sqrt{6}}{5-2\sqrt{6}}}+\sqrt{\frac{5-2\sqrt{6}}{5+2\sqrt{6}}}\)
\(\sqrt{\frac{5+2\sqrt{6}}{5-2\sqrt{6}}}+\sqrt{\frac{5-2\sqrt{6}}{5+2\sqrt{6}}}\)
\(=\sqrt{\frac{3+2\sqrt{3}\sqrt{2}+2}{3-2\sqrt{3}\sqrt{2}+2}}+\sqrt{\frac{3-2\sqrt{3}\sqrt{2}+2}{3+2\sqrt{3}\sqrt{2}+2}}\)
\(=\sqrt{\frac{\left(\sqrt{2}+\sqrt{3}\right)^2}{\left(\sqrt{2}-\sqrt{3}\right)^2}}+\sqrt{\frac{\left(\sqrt{2}-\sqrt{3}\right)^2}{\left(\sqrt{2}+\sqrt{3}\right)^2}}\)
\(=\frac{\left(\sqrt{2}+\sqrt{3}\right)}{\left(\sqrt{2}-\sqrt{3}\right)}+\frac{\left(\sqrt{2}-\sqrt{3}\right)}{\left(\sqrt{2}+\sqrt{3}\right)}\)\
\(=\frac{\left(\sqrt{2}+\sqrt{3}\right)\left(\sqrt{2}+\sqrt{3}\right)+\left(\sqrt{2}-\sqrt{3}\right)\left(\sqrt{2}-\sqrt{3}\right)}{\left(\sqrt{2}-\sqrt{3}\right)\left(\sqrt{2}+\sqrt{3}\right)}\)
\(=\frac{\left(\sqrt{2}+\sqrt{3}\right)^2+\left(\sqrt{2}-\sqrt{3}\right)^2}{\left(\sqrt{2}-\sqrt{3}\right)\left(\sqrt{2}+\sqrt{3}\right)}\)
\(=\frac{5+2\sqrt{6}+5-2\sqrt{6}}{\left(\sqrt{2}-\sqrt{3}\right)\left(\sqrt{2}+\sqrt{3}\right)}\)
\(=10\)
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\(\frac{3+2\sqrt{3}}{\sqrt{3}}+\frac{2+\sqrt{2}}{\sqrt{2}+1}-\left(\sqrt{2}+3\right)\)
\(=\frac{\sqrt{3}\left(\sqrt{3}+2\right)}{\sqrt{3}}+\frac{\sqrt{2}\left(\sqrt{2}+1\right)}{\sqrt{2}+1}-\left(\sqrt{2}+3\right)\)
\(=\sqrt{3}+2+\sqrt{2}-\sqrt{2}-3\)
\(=\sqrt{3}-1\)
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