\(\sqrt{31^{31}}\)và \(\sqrt{17^{29}}\)
so sanh
\(\sqrt{31^{31}}\) và \(\sqrt{17^{39}}\)
giúp mình với ạ
a,\(\sqrt{17-12\sqrt{2}}-\sqrt{17+12\sqrt{2}}\)
b,\(\sqrt{31-12\sqrt{3}}-\sqrt{31+12\sqrt{3}}\)
mình cảm ơn nhiều .
a, \(\sqrt{17-12\sqrt{2}}-\sqrt{17+12\sqrt{2}}\)
\(=\sqrt{17-2.3.2\sqrt{2}}-\sqrt{17+2.3.2\sqrt{2}}\)
\(=\sqrt{9-2.3.2\sqrt{2}+8}-\sqrt{9+2.3.2\sqrt{2}+8}\)
\(=\sqrt{\left(3-2\sqrt{2}\right)^2}-\sqrt{\left(3+2\sqrt{2}\right)^2}=\left|3-2\sqrt{2}\right|-\left|3+2\sqrt{2}\right|\)
\(=3-2\sqrt{2}-3-2\sqrt{2}=-4\sqrt{2}\)
b, \(\sqrt{31-12\sqrt{3}}-\sqrt{31+12\sqrt{3}}\)
\(=\sqrt{31-2.2.3\sqrt{3}}-\sqrt{31+2.2.3\sqrt{3}}\)
\(=\sqrt{\left(3\sqrt{3}-2\right)^2}-\sqrt{\left(3\sqrt{3}+2\right)^2}=\left|3\sqrt{3}-2\right|-\left|3\sqrt{3}+2\right|\)
\(=3\sqrt{3}-2-3\sqrt{3}-2=-4\)
1,\(\sqrt{49-12\sqrt{ }5}+\sqrt{49+12\sqrt{ }5}\)
2,\(\sqrt{29+12\sqrt{ }5}\)+\(\sqrt{29-12\sqrt{ }5}\)
3,\(\sqrt{31-12\sqrt{ }3}-\sqrt{31+12\sqrt{ }3}\)
4,\(\sqrt{39-12\sqrt{ }3}-\sqrt{39+12\sqrt{ }3}\)
Bài 1 : \(\sqrt{49-12\sqrt{5}}+\sqrt{49+12\sqrt{5}}\)
\(=\sqrt{45-4\sqrt{45}+4}+\sqrt{45+4\sqrt{45}+4}\)
\(=\sqrt{\left(\sqrt{45}-2\right)^2}+\sqrt{\left(\sqrt{45}+2\right)^2}\)
\(=\sqrt{45}-2+\sqrt{45}+2=2\sqrt{45}\)
Bài 2 : \(\sqrt{29+12\sqrt{5}}+\sqrt{29-12\sqrt{5}}\)
\(=\sqrt{20+6\sqrt{20}+9}+\sqrt{20-6\sqrt{20}+9}\)
\(=\sqrt{\left(\sqrt{20}+3\right)^2}+\sqrt{\left(\sqrt{20}-3\right)^2}\)
\(=\sqrt{20}+3+\sqrt{20}-3=2\sqrt{20}\)
Bài 3 : \(\sqrt{31-12\sqrt{3}}+\sqrt{31+12\sqrt{3}}\)
\(=\sqrt{27-4\sqrt{27}+4}+\sqrt{27+4\sqrt{27}+4}\)
\(=\sqrt{\left(\sqrt{27}-2\right)^2}+\sqrt{\left(\sqrt{27}+2\right)^2}\)
\(=\sqrt{27}-2+\sqrt{27}+2=2\sqrt{27}\)
Chúc bạn học tốt
4 , Ta có :
\(\sqrt{39-12\sqrt{3}}-\sqrt{39+12\sqrt{3}}\)
\(=\sqrt{3-2.6.\sqrt{3}+6^2}-\sqrt{3+2.6.\sqrt{3}+6^2}\)
\(=\sqrt{\left(\sqrt{3}-6\right)^2}-\sqrt{\left(\sqrt{3}+6\right)^2}\)
\(=\left|\sqrt{3}-6\right|-\left|\sqrt{3}+6\right|\)
\(=6-\sqrt{3}-\sqrt{3}-6\)
\(=-2\sqrt{3}\)
1,\(\sqrt{4-2.2.3\sqrt{5}+45}+\sqrt{4+2.2.3\sqrt{5}+45}\)
\(=\sqrt{\left(2-3\sqrt{5}\right)^2}+\sqrt{\left(2+3\sqrt{5}\right)^2}\)
\(=\left|2-3\sqrt{5}\right|+\left|2+3\sqrt{5}\right|\)
\(=3\sqrt{5}-2+2+3\sqrt{5}\)
\(=6\sqrt{5}\)
không thực hiện phép tính, hãy so sánh giá trị của \(\sqrt{31}+\sqrt{17}+\sqrt{3}\)và 11
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Ta có :
\(\sqrt{31}>\sqrt{30,25}=5.5\)
\(\sqrt{17}>\sqrt{16}=4\)
\(\sqrt{3}>\sqrt{2,25}=1,5\)
Từ điều trên ta có: \(\sqrt{31}+\sqrt{17}+\sqrt{3}>5,5+4+1,5=11\)
Vậy ta có : \(\sqrt{31}+\sqrt{17}+\sqrt{3}>11\)
So sánh hai số sau (không dùng máy tính):
a) 1 và \(\sqrt{2}\)
b) 2 và \(\sqrt{3}\)
c) 6 và \(\sqrt{41}\)
d) 7 và \(\sqrt{47}\)
e) 2 và \(\sqrt{2}+1\)
f) 1 và \(\sqrt{3}-1\)
g) 2\(\sqrt{31}\) và 10
h) \(\sqrt{3}\) và -12
i) -5 và \(-\sqrt{29}\)
giúp e với ạ, em cần gấp
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) \(5=\sqrt{25}< \sqrt{29}\)
\(\Rightarrow-5>-\sqrt{29}\)
So sánh các số:
a) \(\sqrt{5\sqrt{7}}\)và \(\sqrt{7\sqrt{5}}\)
b) \(\sqrt{31}-\sqrt{19}\)và \(6-\sqrt{17}\)
c) \(\sqrt{10}+\sqrt{17}\)và \(\sqrt{61}\)
a \(\left(\sqrt{5\sqrt{7}}\right)^4=\left(\left(\sqrt{5\sqrt{7}}\right)^2\right)^2=\left(5\sqrt{7}\right)^2=25\cdot7=175\)
\(=\left(\sqrt{7\sqrt{5}}\right)^4=\left(\left(\sqrt{7\sqrt{5}}\right)^2\right)^2=\left(7\sqrt{5}\right)^2=49\cdot5=240\)
vì 175<240\(\Rightarrow\left(\sqrt{5\sqrt{7}}\right)^4< \left(\sqrt{7\sqrt{5}}\right)^4\Rightarrow\sqrt{5\sqrt{7}}< \sqrt{7\sqrt{5}}\)
b \(6=\sqrt{36}\)
\(\sqrt{31}< \sqrt{36};\sqrt{19}>\sqrt{17}\Rightarrow\sqrt{31}-\sqrt{19}< \sqrt{36}-\sqrt{17}=6-\sqrt{17}\)
c \(\left(\sqrt{10}+\sqrt{17}\right)^2=10+2\sqrt{10\cdot17}+17=27+2\sqrt{170}\)
\(\left(\sqrt{61}\right)^2=61=27+34=27+2\cdot17=27+2\sqrt{289}\)
vì \(2\sqrt{170}< 2\sqrt{289}\Rightarrow27+2\sqrt{170}< 27+2\sqrt{289}\Rightarrow\left(\sqrt{10}+\sqrt{17}\right)^2< \left(\sqrt{61}\right)^2\)
\(\Rightarrow\sqrt{10}+\sqrt{17}< \sqrt{61}\)
\(\sqrt{31-12\sqrt{3}}-\sqrt{31+12\sqrt{3}}\)
tính
\(\sqrt{31-12\sqrt{3}}-\sqrt{31+12\sqrt{3}}\)
\(=\sqrt{\left(3\sqrt{3}\right)^2-2.3\sqrt{3}.2+2^2}-\sqrt{\left(3\sqrt{3}\right)^2+2.3\sqrt{3}.2+2^2}\)
\(=\sqrt{\left(3\sqrt{3}-2\right)^2}-\sqrt{\left(3\sqrt{3}+2\right)^2}=\left|3\sqrt{3}-2\right|-\left|3\sqrt{3}+2\right|\)
\(=3\sqrt{3}-2-3\sqrt{3}-2=-4\)
\(\sqrt{31-12\sqrt{3}}-\sqrt{31+12\sqrt{3}}\)
=\(\sqrt{27-12\sqrt{3}+4}-\sqrt{27+12\sqrt{3}+4}\)
=\(\sqrt{\left(3\sqrt{3}\right)^2-2.2.3\sqrt{3}+2^2}-\sqrt{\left(3\sqrt{3}\right)^2+2.2.3\sqrt{3}+2^2}\)
=\(\sqrt{\left(3\sqrt{3}-2\right)^2}-\sqrt{\left(3\sqrt{3}+2\right)^2}\)
=\(\left|3\sqrt{3}-2\right|-\left|3\sqrt{3}+2\right|\)
=\(3\sqrt{3}-2-\left(3\sqrt{3}+2\right)\)
=\(3\sqrt{3}-2-3\sqrt{3}-2\)
=-4
\(\sqrt{31-12\sqrt{3}}-\sqrt{31+12\sqrt{3}}\)
\(=3\sqrt{3}-2-3\sqrt{3}-2\)
=-4
tính nhanh
25/37 x 18/29 + 18/29 x 12/37
31/85 x 11/19 + 31/85 x 12/19 - 42/19 x 31/85
c , 16/53 : 17/9 - 16/53 : 17/8
1/5 x 12/31 x 4/3 + 19/31 x 4/15
a) \(\dfrac{25}{37}\times\dfrac{18}{29}+\dfrac{18}{29}\times\dfrac{12}{37}\)
\(=\dfrac{18}{29}\times\left(\dfrac{25}{37}+\dfrac{12}{37}\right)\)
\(=\dfrac{18}{29}\times\dfrac{37}{37}\)
\(=\dfrac{18}{29}\times1\)
\(=\dfrac{18}{29}\)
b) \(\dfrac{31}{85}\times\dfrac{11}{19}+\dfrac{31}{85}\times\dfrac{12}{19}-\dfrac{42}{19}\times\dfrac{31}{85}\)
\(=\dfrac{31}{85}\times\left(\dfrac{11}{19}+\dfrac{12}{19}-\dfrac{42}{19}\right)\)
\(=\dfrac{31}{85}\times\dfrac{-19}{19}\)
\(=\dfrac{31}{85}\times-1\)
\(=-\dfrac{31}{85}\)
c) \(\dfrac{16}{53}:\dfrac{17}{9}-\dfrac{16}{53}:\dfrac{17}{8}\)
\(=\dfrac{16}{53}:\left(\dfrac{9}{17}-\dfrac{8}{17}\right)\)
\(=\dfrac{16}{53}:\dfrac{1}{17}\)
\(=\dfrac{16}{901}\)
c) \(\dfrac{1}{5}\times\dfrac{12}{31}\times\dfrac{4}{3}+\dfrac{19}{31}\times\dfrac{4}{15}\)
\(=\dfrac{4}{15}\times\dfrac{12}{31}+\dfrac{19}{31}\times\dfrac{4}{15}\)
\(=\dfrac{4}{15}\times\left(\dfrac{12}{31}+\dfrac{19}{31}\right)\)
\(=\dfrac{4}{15}\times\dfrac{31}{31}\)
\(=\dfrac{4}{15}\times1\)
\(=\dfrac{4}{15}\)
a: =18/29*(25/37+12/37)
=18/29
b: =31/85(11/19+12/19-42/19)
=-31/85
c; =16/53(9/17+8/17)=16/53
d: =4/15(12/31+19/31)=4/15
so sánh
2 và \(\sqrt{2}\)+ 1
2\(\sqrt{31}\)và 10
\(-3\sqrt{11}\)và - \(\sqrt{12}\)
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 \(-3\sqrt{11}< -\sqrt{12}\)