Ta có :

\(4+\sqrt{33}>4+\sqrt{25}=4+5=9\)

\(\sqrt{29}+\sqrt{14}< \sqrt{25}+\sqrt{9}=5+3=8\)

Vì \(9>8\) nên \(4+\sqrt{33}>\sqrt{29}+\sqrt{14}\)

Vậy \(4+\sqrt{33}>\sqrt{29}+\sqrt{14}\)

Sorry nhầm !!!! làm tại

\(\sqrt{29}+\sqrt{14}< \sqrt{33}+\sqrt{16}=\sqrt{33}+4\)

Vậy \(\sqrt{33}+4>\sqrt{29}+\sqrt{14}\)

=3.74165738 chac 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000%

vo van 

Ta co:\(4+\sqrt{33}=\approx9,744562647\)

\(\sqrt{29}+\sqrt{14}=\approx9,126822194\)

Vi 9,744562647>9,126822194 nen \(4+\sqrt{33}>\sqrt{29}+\sqrt{14}\)

= nhau nha ban

cài đầu tiên lớn hơn

 \(4+\sqrt{33}=\sqrt{16}+\sqrt{33}\)

Có: \(\sqrt{16}>\sqrt{14}\)

\(\sqrt{33}>\sqrt{29}\)

=> \(\sqrt{16}+\sqrt{33}>\sqrt{29}+\sqrt{14}\)

=> \(4+\sqrt{33}>\sqrt{29}+\sqrt{14}\)

a) Ta có: \(4+\sqrt{33}=\sqrt{16}+\sqrt{33}\)

Vì \(\sqrt{16}>\sqrt{14};\sqrt{33}>\sqrt{29}\)

\(\Rightarrow4+\sqrt{33}>\sqrt{29}+\sqrt{14}\)

b) Ta có: \(\sqrt{23}+\sqrt{15}< \sqrt{25}+\sqrt{16}=5+4=9=\sqrt{81}\)

a: \(\left(4+\sqrt{33}\right)^2=49+8\sqrt{33}=49+2\cdot\sqrt{528}\)

\(\left(\sqrt{29}+\sqrt{14}\right)^2=43+2\cdot\sqrt{29\cdot14}=43+2\cdot\sqrt{406}\)

mà 49>43 và 528>406

nên \(\left(4+\sqrt{33}\right)^2>\left(\sqrt{29}+\sqrt{14}\right)^2\)

=>\(4+\sqrt{33}>\sqrt{29}+\sqrt{14}\)

ta có:

căn 36=6

căn 25=5

=>3<căn 33<4

còn lại tự lm nhé!

\(\text{Ta có : }\hept{\begin{cases}4>\sqrt{14}\left(\sqrt{16}>\sqrt{14}\right)\\\sqrt{33}>\sqrt{29}\left(\text{luôn đúng}\right)\end{cases}}\)

\(\Rightarrow4+\sqrt{33}>\sqrt{29}+\sqrt{14}\)

\(\text{Vậy }4+\sqrt{33}>\sqrt{29}+\sqrt{14}\)