\(（\frac{1-\sqrt{2}}{1+\sqrt{2}}-\frac{1+\sqrt{2}}{1-\sqrt{2}}）：\sqrt{72}\)
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VN
1
28 tháng 7 2016
\(\left(\sqrt{4,5}-\frac{1}{2}.\sqrt{72}+5\sqrt{\frac{1}{2}}\right).\left(42\sqrt{\frac{25}{6}}-10\sqrt{\frac{3}{2}}-12\sqrt{\frac{98}{3}}\right)\)
=\(\left(\frac{3\sqrt{2}}{2}-3\sqrt{2}+\frac{5\sqrt{2}}{2}\right).\left(35\sqrt{6}-5\sqrt{6}-28\sqrt{6}\right)\)
=\(\left(\frac{3\sqrt{2}-6\sqrt{2}+5\sqrt{2}}{2}\right).2\sqrt{6}\)
=\(2\sqrt{2}.\sqrt{6}=4\sqrt{3}\)
NV
16 tháng 7 2016
a/ Bạn ghi nhầm đề rồi
c/ \(2\sqrt{18\sqrt{3}}-2\sqrt{5\sqrt{3}}-3\sqrt{5\sqrt{48}}\)
\(=2\sqrt{18}.\sqrt{\sqrt{3}}-2\sqrt{5}.\sqrt{\sqrt{3}}-3\sqrt{5}.\sqrt{\sqrt{48}}\)
\(=2.3\sqrt{2}.\sqrt{\sqrt{3}}-2\sqrt{5}.\sqrt{\sqrt{3}}-3\sqrt{5}.\sqrt{4\sqrt{3}}\)
\(=2.3\sqrt{2}.\sqrt{\sqrt{3}}-2\sqrt{5}.\sqrt{\sqrt{3}}-6\sqrt{5}.\sqrt{\sqrt{3}}\)
\(=2\sqrt{\sqrt{3}}\left(3\sqrt{2}-\sqrt{5}-3\sqrt{5}\right)\)
\(=2\sqrt{\sqrt{3}}\left(3\sqrt{2}-4\sqrt{5}\right)\)\(=2\sqrt{2\sqrt{3}}\left(3-2\sqrt{10}\right)\)
f/ \(\sqrt{2}.\sqrt{2+\sqrt{3}}-2\left(\sqrt{3}-1\right)=\sqrt{4+2\sqrt{3}}-2\left(\sqrt{3}-1\right)\)
\(=\sqrt{\left(\sqrt{3}+1\right)^2}-2\left(\sqrt{3}-1\right)=\left(\sqrt{3}+1\right)-2\left(\sqrt{3}-1\right)\)
\(=\sqrt{3}+1-2\sqrt{3}+2=3-\sqrt{3}=\sqrt{3}\left(\sqrt{3}-1\right)\)
g/ \(\sqrt{5-2\sqrt{6}}+\sqrt{5+2\sqrt{6}}-2\sqrt{3}+2007\)
\(=\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}-2\sqrt{3}+2007\)
\(=\sqrt{3}-\sqrt{2}+\sqrt{3}+\sqrt{2}-2\sqrt{3}+2007\)
\(=2007\)
MM
1
20 tháng 7 2020
Ta có: \(A=\sqrt{72}-6\sqrt{5\frac{1}{3}}+4\sqrt{12\frac{1}{2}}+2\sqrt{27}\)
\(=\sqrt{72}-\sqrt{36\cdot\frac{16}{3}}+\sqrt{16\cdot\frac{25}{2}}+\sqrt{108}\)
\(=\sqrt{72}-\sqrt{192}+\sqrt{200}+\sqrt{108}\)
\(=\left(\sqrt{72}+\sqrt{200}\right)-\left(\sqrt{192}-\sqrt{108}\right)\)
\(=6\sqrt{2}+10\sqrt{2}-\left(8\sqrt{3}-6\sqrt{3}\right)\)
\(=16\sqrt{2}-2\sqrt{3}\)
14 tháng 10 2020
a) \(=\sqrt{\frac{9}{2}}-\sqrt{16.2}+\sqrt{36.2}-\sqrt{81.2}\)
\(=\frac{3}{2}\sqrt{2}-4\sqrt{2}+6\sqrt{2}-9\sqrt{2}\)
\(=\left(\frac{3}{2}-4+6-9\right)\sqrt{2}=\frac{-11}{2}\sqrt{2}\)
b) \(=\frac{\sqrt{5}+3-\sqrt{5}+3}{\left(\sqrt{5}-3\right)\left(\sqrt{5}+3\right)}.\frac{\sqrt{3}\left(\sqrt{3}-1\right)}{1-\sqrt{3}}\)
\(=\frac{6}{5-9}.\left(-\sqrt{3}\right)=\frac{3}{2}\sqrt{3}\)
c) \(=\left(\frac{a-1-4\sqrt{a}+\sqrt{a}+1}{a-1}\right):\frac{\sqrt{a}\left(\sqrt{a}-2\right)}{a-1}\)
\(=\frac{a-3\sqrt{a}}{a-1}.\frac{a-1}{\sqrt{a}\left(\sqrt{a}-2\right)}\)
\(=\frac{\sqrt{a}\left(\sqrt{a}-3\right)}{\sqrt{a}\left(\sqrt{a}-2\right)}=\frac{\sqrt{a}-3}{\sqrt{a}-2}\)
\(\left(\frac{1-\sqrt{2}}{1+\sqrt{2}}-\frac{1+\sqrt{2}}{1-\sqrt{2}}\right):\sqrt{72}\)
\(\left[\frac{\left(1-\sqrt{2}\right)^2-\left(1+\sqrt{2}\right)^2}{\left(1+\sqrt{2}\right)\left(1-\sqrt{2}\right)}\right]:\sqrt{72}\)
\(=\frac{1-2\sqrt{2}+2-1-2\sqrt{2}-2}{1-2}\cdot\frac{1}{\sqrt{72}}\)
\(=\frac{-2\sqrt{2}-2\sqrt{2}}{-1}\cdot\frac{1}{\sqrt{72}}\)
\(=4\sqrt{2}\cdot\frac{1}{2\sqrt{18}}=\frac{2}{\sqrt{9}}=\frac{2}{3}\)