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a)
Có: \(2>1>0\)
\(\Rightarrow\sqrt{2}>1\Rightarrow1+\sqrt{2}>1+1\\ \Leftrightarrow1+\sqrt{2}>2\)
b) Có: \(0< \sqrt{3}< 3\)
\(\Rightarrow3+1>\sqrt{3}+1\\ \Rightarrow4>\sqrt{3}+1\)
c) Có: \(0< \sqrt{11}< \sqrt{25}\left(0< 11< 25\right)\)
\(\Rightarrow\sqrt{11}< 5\\ \Rightarrow-2\sqrt{11}>-2.5=-10\left(-2< 0\right)\)
d) Có: \(0< \sqrt{11}< \sqrt{16}=4\left(do.0< 11< 16\right)\)
\(\Rightarrow3\sqrt{11}< 3.4\\ \Leftrightarrow3\sqrt{11}< 12\)
a: 2=1+1<1+căn 2
b: 4=1+3>1+căn 3
c: -2căn 11=-căn 44
-10=-căn 100
mà 44<100
nên -2 căn 11>-10
d: 12=3*4=3*căn 16>3*căn 11
a: \(1< \sqrt{2}\)
nên \(2< \sqrt{2}+1\)
b: \(2\sqrt{31}=\sqrt{124}\)
\(10=\sqrt{100}\)
mà 124>100
nên \(2\sqrt{31}>10\)
c: \(-3\sqrt{11}=-\sqrt{99}\)
\(-\sqrt{12}=-\sqrt{12}\)
mà 99>12
nên \(-3\sqrt{11}< -\sqrt{12}\)
a) \(1=\sqrt{1}< \sqrt{2}\)
b) \(2=\sqrt{4}>\sqrt{3}\)
c) \(6=\sqrt{36}< \sqrt{41}\)
d) \(7=\sqrt{49}>\sqrt{47}\)
e) \(2=1+1=\sqrt{1}+1< \sqrt{2}+1\)
f) \(1=2-1=\sqrt{4}-1>\sqrt{3}-1\)
g) \(2\sqrt{31}=\sqrt{4.31}=\sqrt{124}>\sqrt{100}=10\)
h) \(\sqrt{3}>0>-\sqrt{12}\)
i) \(5=\sqrt{25}< \sqrt{29}\)
\(\Rightarrow-5>-\sqrt{29}\)
a) Ta có: \(2=\sqrt{4}\)
Vì \(4>3\Rightarrow\sqrt{4}>\sqrt{3}\Rightarrow2>\sqrt{3}\Rightarrow1>\sqrt{3}-1\)
b) \(\left\{{}\begin{matrix}2\sqrt{31}=\sqrt{4.31}=\sqrt{124}\\10=\sqrt{100}\end{matrix}\right.\)
Vì \(124>100\Rightarrow\sqrt{124}>\sqrt{100}\Rightarrow2\sqrt{31}>10\)
c) Vì \(15< 16\Rightarrow\sqrt{15}< \sqrt{16}\Rightarrow\sqrt{15}-1< \sqrt{16}-1\)
\(\Rightarrow\sqrt{15}-1< 4-1\Rightarrow\sqrt{15}-1< 3\)
Lại có: \(10>9\Rightarrow\sqrt{10}>\sqrt{9}\Rightarrow\sqrt{10}>3\)
\(\Rightarrow\sqrt{10}>\sqrt{15}-1\)
a, \(1< 2\Rightarrow\sqrt{1}< \sqrt{2}\Rightarrow1+1< \sqrt{2}+1\Rightarrow2< \sqrt{2}+1\)
c, \(4>3=>\sqrt{4}>\sqrt{3}=>\sqrt{4}-1>\sqrt{3}-1\Rightarrow1>\sqrt{3}-1\)
d, \(16>11=>\sqrt{16}>\sqrt{11}\Rightarrow4>\sqrt{11}=>4.\left(-3\right)< \sqrt{11}.\left(-3\right)\)
\(=>-12< -3.\sqrt{11}\)
a) Ta có:
\(2=1+1=1+\sqrt{1}\)
Mà: \(1< 2\Rightarrow\sqrt{1}< \sqrt{2}\)
\(\Rightarrow1+\sqrt{1}< \sqrt{2}+1\)
\(\Rightarrow2< \sqrt{2}+1\)
b) Ta có:
\(1=2-1=\sqrt{4}-1\)
Mà: \(4>3\Rightarrow\sqrt{4}>\sqrt{3}\)
\(\Rightarrow\sqrt{4}-1>\sqrt{3}-1\)
\(\Rightarrow1>\sqrt{3}-1\)
c) Ta có:
\(10=2\cdot5=2\sqrt{25}\)
Mà: \(25< 31\Rightarrow\sqrt{25}< \sqrt{31}\)
\(\Rightarrow2\sqrt{25}< 2\sqrt{31}\)
\(\Rightarrow10< 2\sqrt{31}\)
d) Ta có:
\(-12=-3\cdot4=-3\sqrt{16}\)
Mà: \(16>11\Rightarrow\sqrt{16}>\sqrt{11}\)
\(\Rightarrow-3\sqrt{16}< -3\sqrt{11}\)
\(\Rightarrow-12< -3\sqrt{11}\)