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}`
