SO SANH
\(-2\sqrt{5}va-5\sqrt{2}\)
so sanh
\(2\sqrt{5}-5\)va \(\sqrt{5}-3\)
\(\sqrt{17}+\sqrt{26}\) va 9
a ) \(2\sqrt{5}-5\) và \(\sqrt{5}-3\)
Ta có ; \(2\sqrt{5}-5-\left(\sqrt{5}-3\right)\)
\(=\sqrt{5}-8\)
\(=\sqrt{5}-\sqrt{64}< 0\)
\(\Rightarrow2\sqrt{5}-5< \sqrt{5}-3\)
Vậy .................
b ) \(\sqrt{17}+\sqrt{26}\) và 9
Ta có :
\(\sqrt{17}>\sqrt{16}\)
\(\sqrt{26}>\sqrt{25}\)
\(\Rightarrow\sqrt{17}+\sqrt{26}>\sqrt{16}+\sqrt{25}=4+5=9\)
Vậy ...
So sanh:
a, \(\sqrt{\dfrac{35}{34}}\) va \(\sqrt{\dfrac{71}{70}}\)
b, \(4\sqrt{5}-3\sqrt{2}\) va 5
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bai 4 so sanh cac so thuc
\(\frac{4}{9}va\)0,4(5)
\(\sqrt[2]{3}va\sqrt[3]{2}\)
so sanh \(\sqrt{5}+\sqrt{7}\) va 2\(\sqrt{6}\)
giai full giup minh nhe!thanks
Ta có : \(\left(\sqrt{5}+\sqrt{7}\right)^2=5+7+2\sqrt{35}\)
=\(12+2\sqrt{35}\le12+2\sqrt{36}=12+2.6=24\)
Mà \(\left(2\sqrt{6}\right)^2=24\)
Do đó \(\left(\sqrt{5}+\sqrt{7}\right)^2< \left(2\sqrt{6}\right)^2\)
Mà \(\sqrt{5}+\sqrt{7}>0\) và \(2\sqrt{6}>0\)
Vậy \(\sqrt{5}+\sqrt{7}< 2\sqrt{6}\)
so sanh
a) 2^90 va 5^36
b) 99^200 va 9999^100
c) 2^150 va 3^100
d) \(\sqrt{26+2}\) va \(\sqrt{26}\)+ \(\sqrt{2}\)
so sanh x va y biet
a) x=\(2\sqrt{7}\)va y=\(3\sqrt{3}\)
b) x=\(6\sqrt{2}\)va y=\(5\sqrt{3}\)
c) x=\(\sqrt{31}-\sqrt{33}\) va y=\(6-\sqrt{11}\)
so sanh ko dung may tinh
1 )\(\sqrt{3}\) +\(\sqrt{7}\) va 2+ \(\sqrt{6}\)
2) \(\sqrt{7}\) - \(\sqrt{5}\) va \(\sqrt{6}-2\)
3) \(\sqrt{11}-\sqrt{7}vs\sqrt{7}-\sqrt{3}\)
1: \(\left(\sqrt{3}+\sqrt{7}\right)^2=10+2\sqrt{21}\)
\(\left(2+\sqrt{6}\right)^2=10+4\sqrt{6}\)
mà 2 căn 21<4 căn 6
nên căn 3+căn 7<2+căn 6
2: \(\sqrt{7}-\sqrt{5}=\dfrac{2}{\sqrt{7}+\sqrt{5}}\)
\(\sqrt{6}-2=\dfrac{2}{\sqrt{6}+2}\)
mà \(\sqrt{7}+\sqrt{5}>\sqrt{6}+2\)
nên \(\sqrt{7}-\sqrt{5}< \sqrt{6}-2\)
3: \(\sqrt{11}-\sqrt{7}=\dfrac{4}{\sqrt{11}+\sqrt{7}}\)
\(\sqrt{7}-\sqrt{3}=\dfrac{4}{\sqrt{7}+\sqrt{3}}\)
mà căn 11>căn 3
nên \(\sqrt{11}-\sqrt{7}< \sqrt{7}-\sqrt{3}\)
so sanh \(\sqrt{8}\)va \(\sqrt{5}\)+1
có \(\sqrt{8}\)<\(\sqrt{9}\)=3
\(\sqrt{5}\)+1>\(\sqrt{4}\)+1=3
suy ra \(\sqrt{5}\)+1>\(\sqrt{8}\)
so sanh :\(\sqrt{1999}+\sqrt{2001}..va..2\sqrt{2000}\)