Question

Hãy so sánh các cặp số sau :

a) \(\sqrt{17}\) và \(\sqrt[3]{28}\)

b) \(\sqrt[4]{13}\) và \(\sqrt[5]{23}\)

c) \(\left(\dfrac{1}{3}\right)^{\sqrt{3}}\) và \(\left(\dfrac{1}{3}\right)^{\sqrt{2}}\)

d) \(4^{\sqrt{5}}\) và \(4^{\sqrt{7}}\)

Answer 1

a) \(\left(\sqrt{17}\right)^6=\sqrt{\left(17^3\right)^2}=17^3=4913\)

\(\left(\sqrt[3]{28}\right)^6=\sqrt[3]{\left(28^2\right)^3}=28^2=784\)

=> \(\left(\sqrt{17}\right)^6>\left(\sqrt[3]{28}\right)^6\)

=> \(\sqrt{17}>\sqrt[3]{28}\)

Answer 2

b) \(\left(\sqrt[4]{13}\right)^{20}=13^5=371293\)

\(\left(\sqrt[5]{23}\right)^{20}=23^4=279841\)

=> \(\sqrt[4]{13}>\sqrt[5]{23}\)

Answer 3

a)\(\sqrt{3}>\sqrt{2}\) => \(3^{\sqrt{3}}>3^{\sqrt{2}}\)

=> \(\dfrac{1}{3^{\sqrt{3}}}< \dfrac{1}{3^{\sqrt{2}}}\)

\(\Leftrightarrow\left(\dfrac{1}{3}\right)^{\sqrt{3}}< \left(\dfrac{1}{3}\right)^{\sqrt{2}}\)

Answer 4

d) \(\sqrt{5}< \sqrt{7}\)

=> \(4^{\sqrt{5}}< 4^{\sqrt{7}}\)

Answer 5

\(\)\(\sqrt[4]{3}\)

Answer 6

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