a)

 \(\dfrac{5}{9}< \dfrac{9}{9}\)

\(\dfrac{8}{7}>\dfrac{7}{7}\)

\(\dfrac{9}{9}=1\)

\(\dfrac{18}{4}>\dfrac{3}{4}\)

b) 

\(\dfrac{2}{5},\dfrac{3}{5},\dfrac{8}{5}\)

\(\dfrac{5}{2}=\dfrac{15}{6},\dfrac{1}{6},1=\dfrac{6}{6}\rightarrow\dfrac{1}{6},\dfrac{6}{6},\dfrac{15}{6}\)

a) 5/8 < 7/8

b) 15/25 < 4/5 

 5/8 < 7/8

 15/25  <  4/5

   (Quy đồng như sau )

 15          15  x  5            75                                                       4                  4  x  25             100

____ = ___________=____                                               ________=_____________=________

 25            25 x  5            125                                                      5                5  x  25               100

\(\Leftrightarrow\frac{25}{48}.2=\frac{34}{69}.2\)

\(\Leftrightarrow\frac{25}{24}\text{và}\frac{68}{69}\)

mà\(\frac{25}{24}>1\)

     \(\frac{68}{69}< 1\)

\(\Rightarrow\frac{25}{24}>\frac{68}{69}\)

\(\Rightarrow\frac{25}{48}>\frac{34}{69}\)

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 \(\frac{15-2\sqrt{10}}{3}< \sqrt{15}\)

Jdkdk

Jidkri

a)Ta có :\(3^{60}=\left(3^3\right)^{20}=27^{20}\)

\(2^{80}=\left(2^4\right)^{20}=16^{20}\)

Mà \(27^{20}>16^{20}\Leftrightarrow3^{60}>2^{80}\)

b)Ta có :\(5^{20}=\left(5^4\right)^5=625^5\)

\(4^{25}=\left(4^5\right)^5=1024^5\)

Mà \(1024^5>625^5\Leftrightarrow5^{20}< 4^{25}\)

a) \(\frac{3}{-4}=\frac{-3}{4};\frac{-1}{-4}=\frac{1}{4}\)

Vì - 3 < 1 nên \(\frac{-3}{4}< \frac{1}{4}\)

hay \(\frac{3}{-4}< \frac{-1}{-4}\)

Quy đồng mẫu ta được:

15/17=15.27/17.27=405/459

25/27=25.17/27.27=425/459

⇒405/459<425/459⇒15/17<25/27

c) quy đồng

-9/6=-36/24

6/-4=36/-24

tương đương -36/24=-36/24

suy ra -9/6=6/-4

1.a) 3/4 > 5/10

   b) 35/25 > 16/14

2.a) 7/5 > 5/7

  b) 14/16 < 24/21

HT nha

( bạn t.i.c.k cho mik nha, mik cảm ơn )

Tyyyyn

Bạn giúp mình câu này nhé so sánh 317/633 và 371/743 

Ta có

\(\frac{13}{27}:\frac{13}{27}=1\)

\(\frac{7}{15}:\frac{13}{27}=\frac{63}{65}\)

Mặt khác \(\frac{63}{65}< 1\)

\(\Rightarrow\frac{13}{27}:\frac{13}{27}>\frac{7}{15}:\frac{23}{27}\)

\(\Rightarrow\frac{13}{27}:\frac{13}{27}\times\frac{13}{27}>\frac{7}{15}:\frac{23}{27}\times\frac{13}{27}\)

\(\Rightarrow\frac{13}{27}>\frac{7}{15}\)