Đáp án:

`a)` ` 11>\sqrt{113}`

`b)` `\sqrt{37}-\sqrt{15}>2`

`c)` `\sqrt{24}+\sqrt{45}<12`

`d)` `\sqrt{33}-\sqrt{17}<6-\sqrt{15}`

Giải thích các bước giải:

`a)` Ta có: 

`\qquad 11= \sqrt{11^2}=\sqrt{121}`

Vì `121>113=>\sqrt{121}>\sqrt{113}`

`=>11>\sqrt{113}`

$\\$

`b)` Vì `37>36=>\sqrt{37}>\sqrt{36}`

`\qquad 15<16=>\sqrt{15}<\sqrt{16}`

`=>-\sqrt{15}> -\sqrt{16}`

`=> \sqrt{37}-\sqrt{15}>\sqrt{36}-\sqrt{16}`

`>\sqrt{6^2}-\sqrt{4^2}=6-4=2`

Vậy: `\sqrt{37}-\sqrt{15}>2`

$\\$

`c)` Vì `24<25=>\sqrt{24}<\sqrt{25}`

`\qquad 45<49=>\sqrt{45}<\sqrt{49}`

`=> \sqrt{24}+\sqrt{45}<\sqrt{25}+\sqrt{49}`

`<\sqrt{5^2}+\sqrt{7^2}=5+7=12`

Vậy: `\sqrt{24}+\sqrt{45}<12`

$\\$

`d)` Vì `33<36=>\sqrt{33}<\sqrt{36}`

`\qquad 17>15=>\sqrt{17}>\sqrt{15}`

`=>-\sqrt{17}<-\sqrt{15}`

`=>\sqrt{33}-\sqrt{17}<\sqrt{36}-\sqrt{15}`

`<\sqrt{6^2}-\sqrt{15}=6-\sqrt{15}`

Vậy: `\sqrt{33}-\sqrt{17}<6-\sqrt{15}`