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\(\sqrt[3]{\left(1-\sqrt{3}\right)\left(4-2\sqrt{3}\right)}=\sqrt[3]{\left(1-\sqrt{3}\right)\left(\sqrt{3}-1\right)^2}\)=\(\sqrt[3]{\left(1-\sqrt{3}\right)^3}\)=1-\(\sqrt{3}\)
\(\sqrt[3]{\left(1-\sqrt{5}\right)\left(6-2\sqrt{5}\right)}=\sqrt[3]{\left(1-\sqrt{5}\right)\left(\sqrt{5}-1\right)^2}\)=\(\sqrt[3]{\left(1-\sqrt{5}\right)^3}\)=1-\(\sqrt{5}\)
Ta thấy \(\sqrt{5}>\sqrt{3}\)nên 1-\(\sqrt{3}\)>\(1-\sqrt{5}\)
Vậy \(\sqrt[3]{\left(1-\sqrt{3}\right)\left(4-2\sqrt{3}\right)}\)>\(\sqrt[3]{\left(1-\sqrt{5}\right)\left(6-2\sqrt{5}\right)}\)
a)7/23<11/28
b)2014/2015+2015/2016>2014+2015/2015+2016
c) A= gì vậy
1) \(A=\left(\sqrt{7-\sqrt{21}+4\sqrt{5}}\right)^2=7-\sqrt{21}+4\sqrt{5}\)
\(B=\left(\sqrt{5}-1\right)^2=6-2\sqrt{5}\)
\(\Rightarrow A-B=1-\sqrt{21}+6\sqrt{5}=\left(1+\sqrt{180}\right)-\sqrt{21}>0\)
\(\Rightarrow A>B\Rightarrow\sqrt{7-\sqrt{21}+4\sqrt{5}}>\sqrt{5}-1\)
2) \(C=\left(\sqrt{5}+\sqrt{10}+1\right)^2=5+10+1+10\sqrt{2}+2\sqrt{5}+2\sqrt{10}\)
\(=26+10\sqrt{2}+2\sqrt{5}+2\sqrt{10}>26+10>35=\left(\sqrt{35}\right)^2\)
Vậy \(\sqrt{5}+\sqrt{10}+1>\sqrt{35}\)
3) \(\left(\frac{15-2\sqrt{10}}{3}\right)^2=\frac{225-60\sqrt{10}+40}{9}=\frac{265-60\sqrt{10}}{9}=\frac{265}{9}-\frac{20\sqrt{10}}{3}< 15\)
Vậy nên \(\frac{15-2\sqrt{10}}{3}< \sqrt{15}\)
a) Ta có: \(\frac{1}{5}\sqrt{150}=\frac{1}{5}\cdot5\sqrt{6}=\sqrt{6}=\frac{1}{3}\cdot\sqrt{6\cdot9}=\frac{1}{3}\sqrt{54}>\frac{1}{3}\sqrt{51}\)
b) Ta có: \(\frac{1}{2}\sqrt{6}=\sqrt{\frac{6}{4}}< \sqrt{\frac{36}{2}}=6\sqrt{\frac{1}{2}}\)
a) Vì \(5,\left(6\right)< 6\)\(\Rightarrow\)\(\frac{51}{9}< \frac{150}{25}\)
\(\Rightarrow\)\(\sqrt{\frac{51}{9}}< \sqrt{\frac{150}{25}}\)
\(\Rightarrow\)\(\frac{1}{3}\sqrt{51}< \frac{1}{5}\sqrt{150}\)
b) Vì \(1,5< 18\)\(\Rightarrow\)\(\frac{6}{4}< \frac{36}{2}\)
\(\Rightarrow\)\(\sqrt{\frac{6}{4}}< \sqrt{\frac{36}{2}}\)
\(\Rightarrow\)\(\frac{1}{2}\sqrt{6}< 6\sqrt{\frac{1}{2}}\)
So Sánh
a.\(\dfrac{1}{4}\sqrt{8}\) và \(\dfrac{2}{3}\sqrt{12}\)
Có:\(\dfrac{1}{4}\sqrt{8}\) và \(\dfrac{2}{3}\sqrt{12}\)
= \(\dfrac{1}{4}.2\sqrt{2}\) và \(\dfrac{2}{3}.2\sqrt{3}\)
=\(\dfrac{\sqrt{2}}{2}\)và \(\dfrac{4\sqrt{3}}{3}\)
=> \(\dfrac{1}{4}\sqrt{8}< \dfrac{2}{3}\sqrt{12}\)
b. \(\dfrac{5}{2}\sqrt{\dfrac{1}{6}}\)và \(6\sqrt{\dfrac{1}{35}}\)
Có \(\dfrac{5}{2}\sqrt{\dfrac{1}{6}}\) và \(6\sqrt{\dfrac{1}{35}}\)
=\(\dfrac{5}{2}.\dfrac{\sqrt{6}}{6}\) và \(6.\dfrac{\sqrt{35}}{35}\)
=\(\dfrac{5\sqrt{6}}{12}\) và \(\dfrac{6\sqrt{35}}{35}\)
=> \(\dfrac{5}{2}\sqrt{\dfrac{1}{6}}>6\sqrt{\dfrac{1}{35}}\)
c. \(\dfrac{1}{6}\sqrt{18}\) và \(\dfrac{1}{2}\sqrt{2}\)
=\(\dfrac{1}{6}.3\sqrt{2}\) và \(\dfrac{1}{2}\sqrt{2}\)
=\(\dfrac{\sqrt{2}}{2}\) và \(\dfrac{\sqrt{2}}{2}\)
=> \(\dfrac{1}{6}\sqrt{18}=\dfrac{1}{2}\sqrt{2}\)
