\(\sqrt{50}+\sqrt{37}+\sqrt{101}>\sqrt{49}+\sqrt{100}+\sqrt{36}=7+6+10=23=\sqrt{529}\)

\(\frac{\frac{5}{5}+\frac{5}{35}-\frac{6}{125}-\frac{6}{2009}-\frac{6}{2011}}{\frac{7}{5}+\frac{7}{35}-\frac{7}{125}-\frac{7}{2009}-\frac{7}{2011}}=\frac{5\left(\frac{1}{5}+\frac{1}{35}-\frac{1}{125}-\frac{1}{2009}-\frac{1}{2011}\right)}{7\left(\frac{1}{5}+\frac{1}{35}-\frac{1}{125}-\frac{1}{2009}-\frac{1}{2011}\right)}=\frac{5}{7}\)

Ta có: \(\sqrt{529}=\sqrt{23^2}=23\)

Thấy: \(\sqrt{37}>\sqrt{36}\); \(\sqrt{50}>\sqrt{49}\); \(\sqrt{101}>\sqrt{100}\)

\(\Rightarrow\sqrt{37}+\sqrt{50}+\sqrt{101}>\sqrt{36}+\sqrt{49}+\sqrt{100}=6+7+10=23\)

Mà \(\sqrt{529}=23\) \(\Rightarrow\sqrt{37}+\sqrt{50}+\sqrt{101}>\sqrt{529}\)

\(71^{50}=71^{2.25}=\left(71^2\right)^{25}=5041^{25}\\ 37^{75}=37^{3.25}=\left(37^3\right)^{25}=50653^{25}\\ Vì:5041^{25}< 50653^{25}\Rightarrow71^{50}< 37^{75}\)

71⁵⁰ = (71²)²⁵ = 5041²⁵

37⁷⁵ = (37³)²⁵ = 50653²⁵

Do 5041 < 50653 nên 5041²⁵ < 50653²⁵

Vậy 71⁵⁰ < 37⁷⁵

=(71^2)^25 và (37^3)^25

=5041^25 và 50653^25

vì 5041^25<50653^25

suy ra:71^50<37^75

\(\dfrac{49}{50}< 1< \dfrac{101}{97}\)

71⁵⁰=(71²)²⁵=5041²⁵

37⁷⁵=(37³)²⁵=50653²⁵

vì 5041²⁵<50653²⁵ nên 71⁵⁰<37⁷⁵

tick nhé bạn không bik đúng hay sai nữa

So sánh 71⁵⁰ và 37⁷⁵

71⁵⁰=71^2.25=(71²)²⁵=5041²⁵

37⁷⁵=37^3.25=(37³)²⁵=50653²⁵

Vì 5041²⁵ < 50653²⁵

Nên 71⁵⁰ < 37⁷⁵

k cho huynh van hieu di

So sánh 7150 và 3775

7150=712.25=(712)25=504125

3775=373.25=(373)25=5065325

Vì 504125 < 5065325

Nên 7150 < 3775

7150=(712)25=504125

3775=(373)25=5065325

vì 504125<5065325 nên 7150<3775

7150=(712)25=504125

3775=(373)25=5065325

vì 504125<5065325 nên 7150<3775