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CC
0
VH
1
24 tháng 7 2016
Ta có : \(\frac{3\sqrt{3}}{\sqrt{2}+\sqrt{3}+\sqrt{5}}=\frac{3\sqrt{3}\left(\sqrt{2}+\sqrt{3}-\sqrt{5}\right)}{\left(\sqrt{2}+\sqrt{3}+\sqrt{5}\right)\left(\sqrt{2}+\sqrt{3}-\sqrt{5}\right)}\)
\(=\frac{3\sqrt{3}\left(\sqrt{2}+\sqrt{3}+\sqrt{5}\right)}{\left(\sqrt{2}+\sqrt{3}\right)^2-\left(\sqrt{5}\right)^2}=\frac{3\sqrt{3}\left(\sqrt{2}+\sqrt{3}+\sqrt{5}\right)}{2\sqrt{6}}\)
\(=\frac{3\left(\sqrt{2}+\sqrt{3}+\sqrt{5}\right)}{2\sqrt{2}}=\frac{3\sqrt{2}\left(\sqrt{2}+\sqrt{3}+\sqrt{5}\right)}{4}\)
3 tháng 8 2020
a/ \(\frac{1}{2+\sqrt{3}}-\frac{1}{2-\sqrt{3}}+5\sqrt{3}\)
\(=\frac{2-\sqrt{3}}{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}-\frac{2+\sqrt{3}}{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}+5\sqrt{3}\)
\(=\frac{2-\sqrt{3}}{4-3}-\frac{2+\sqrt{3}}{4-3}+5\sqrt{3}\)
\(=2-\sqrt{3}-2-\sqrt{3}+5\sqrt{3}\)
\(=3\sqrt{3}\)
Vậy..
3 tháng 8 2020
b/ \(\frac{1}{\sqrt{5}+2}-\sqrt{9+4\sqrt{5}}\)
\(=\frac{1}{\sqrt{5}+2}-\sqrt{\left(\sqrt{5}+2\right)^2}\)
\(=\frac{1}{\sqrt{5}+2}-\left|\sqrt{5}+2\right|\)
\(=\frac{\sqrt{5}-2}{\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)}-\sqrt{5}-2\)
\(=\sqrt{5}-2-\sqrt{5}-2\)
\(=-4\)
Vậy..
2 tháng 7 2019
\(a,\frac{\sqrt{5}}{\sqrt{3-\sqrt{5}}}=\frac{\sqrt{5}\left(\sqrt{3+\sqrt{5}}\right)}{\sqrt{\left(3-\sqrt{5}\right).\left(3+\sqrt{5}\right)}}\)
\(=\frac{\sqrt{5}\left(\sqrt{3+\sqrt{5}}\right)}{\sqrt{9-5}}=\frac{\sqrt{5}\left(\sqrt{3+\sqrt{5}}\right)}{\sqrt{4}}=\frac{\sqrt{5}\left(\sqrt{3+\sqrt{5}}\right)}{2}\)
TH
2
19 tháng 9 2016
\(\frac{1}{\sqrt{2}+\sqrt{3}+\sqrt{5}}=\frac{\sqrt{2}+\sqrt{3}-\sqrt{5}}{\left(\sqrt{2}+\sqrt{3}+\sqrt{5}\right)\left(\sqrt{2}+\sqrt{3}-\sqrt{5}\right)}\)
\(=\frac{\sqrt{2}+\sqrt{3}-\sqrt{5}}{\left(\sqrt{2}+\sqrt{3}\right)^2-\left(\sqrt{5}\right)^2}=\frac{\sqrt{2}+\sqrt{3}-\sqrt{5}}{2+2\sqrt{2\cdot3}+3-5}=\frac{\sqrt{2}+\sqrt{3}-\sqrt{5}}{5+2\sqrt{6}-5}=\frac{\sqrt{6}\cdot\left(\sqrt{2}+\sqrt{3}-\sqrt{5}\right)}{\sqrt{6}\cdot2\sqrt{6}}=\frac{2\sqrt{3}+3\sqrt{2}-\sqrt{30}}{12}\)
18 tháng 9 2016
Ta có \(\frac{1}{\sqrt{2}+\sqrt{3}+\sqrt{5}}\) = \(\frac{\sqrt{2}+\sqrt{3}-\sqrt{5}}{5+2\sqrt{6}-5}\)
= \(\frac{\sqrt{6}\left(\sqrt{2}+\sqrt{3}-\sqrt{5}\right)}{12}\)
YY
0
PT
1
15 tháng 7 2016
\(\frac{3+4\sqrt{3}}{\sqrt{6}+\sqrt{2}-\sqrt{5}}=\frac{\left(3+4\sqrt{3}\right)\left(\sqrt{6}+\sqrt{2}+\sqrt{5}\right)}{\left(\sqrt{6}+\sqrt{2}-\sqrt{5}\right)\left(\sqrt{6}+\sqrt{2}+\sqrt{5}\right)}\)
\(=\frac{\left(3+4\sqrt{3}\right)\left(\sqrt{6}+\sqrt{2}+\sqrt{5}\right)}{\left(\sqrt{6}+\sqrt{2}\right)^2-\left(\sqrt{5}\right)^2}=\frac{\left(3+4\sqrt{3}\right)\left(\sqrt{6}+\sqrt{2}+\sqrt{5}\right)}{3+4\sqrt{3}}=\sqrt{6}+\sqrt{2}+\sqrt{5}\)
19 tháng 6 2019
a) \(\frac{9}{\sqrt{3}}=\frac{9\sqrt{3}}{3}=3\sqrt{3}\)
b) \(\frac{3}{\sqrt{5}-\sqrt{2}}=\frac{3\left(\sqrt{5}+\sqrt{2}\right)}{\left(\sqrt{5}-\sqrt{2}\right)\left(\sqrt{5}+\sqrt{2}\right)}=\frac{3\left(\sqrt{5}+\sqrt{2}\right)}{5-2}=\sqrt{5}+\sqrt{2}\)
c) \(\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}=\frac{\left(\sqrt{5}-\sqrt{3}\right)^2}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}=\frac{5-2\sqrt{15}+3}{5-3}=\frac{8-2\sqrt{15}}{2}=4-\sqrt{15}\)
d) \(\frac{1}{\sqrt{18}+\sqrt{8}-2\sqrt{2}}=\frac{1}{3\sqrt{2}+2\sqrt{2}-2\sqrt{2}}=\frac{1}{3\sqrt{2}}=\frac{\sqrt{2}}{3\sqrt{2}\cdot\sqrt{2}}=\frac{\sqrt{2}}{6}\)
\(A=\frac{\sqrt{5}+\sqrt{3}}{\sqrt{2}}=\frac{\sqrt{2}\left(\sqrt{5}+\sqrt{3}\right)}{2}=\frac{\sqrt{10}+\sqrt{6}}{2}\)