\(\sqrt{3}-\sqrt{27}-\sqrt{144}:\sqrt{36}\)
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3 tháng 7 2018
\(\sqrt{3\cdot27}-\sqrt{\dfrac{144}{36}}\)=\(\sqrt{81}-\sqrt{4}\)=9-2=7
\(\dfrac{2\cdot3+3\cdot6}{4}\)=6
\(\sqrt{7}-\sqrt{7-2\cdot\sqrt{7}+1}\)=\(\sqrt{7}-\left(\sqrt{7}-1\right)\)=1
\(\dfrac{\sqrt{3-2\cdot\sqrt{3}+1}}{\sqrt{2}\cdot\left(\sqrt{3}-1\right)}\)=\(\dfrac{\sqrt{3}-1}{\sqrt{2}\cdot\left(\sqrt{3}-1\right)}\)=\(\dfrac{1}{\sqrt{2}}\)
\(\dfrac{\sqrt{5}\cdot\left(\sqrt{5}+3\right)}{\sqrt{5}}\)+\(\dfrac{\sqrt{3}\cdot\left(1+\sqrt{3}\right)}{\sqrt{3}+1}\)-(\(\sqrt{5}+3\))
=(\(\sqrt{5}+3\))+\(\sqrt{3}\)-(\(\sqrt{5}+3\))=\(\sqrt{3}\)
\(\sqrt{3}\cdot\sqrt{9}+5\cdot\sqrt{4}\cdot3-2\sqrt{3}\)
=\(\sqrt{3}\cdot\left(3+10-2\right)\)
=\(11\sqrt{3}\)
18 tháng 9 2021
\(3\sqrt{144}-5\sqrt{49}+\dfrac{1}{2}\sqrt{36}\)
\(=3.12-5.7+\dfrac{1}{2}.6\)
\(=36-35+3=4\)
TH
D = \(\frac{\sqrt{3}+\sqrt{4}+\sqrt{5}}{\sqrt{6}+\sqrt{8}+\sqrt{10}+\sqrt{27}+\sqrt{36}+\sqrt{45}}\)
1
20 tháng 7 2017
=\(\frac{\sqrt{3}+\sqrt{4}+\sqrt{5}}{\sqrt{2}\left(\sqrt{3}+\sqrt{4}+\sqrt{5}\right)+3\left(\sqrt{3}+\sqrt{4}+\sqrt{5}\right)}\)
=\(\frac{\sqrt{3}+\sqrt{4}+\sqrt{5}}{\left(\sqrt{2}+3\right)\left(\sqrt{3}+\sqrt{4}+\sqrt{5}\right)}=\frac{1}{\sqrt{2}+3}\)=\(\frac{3-\sqrt{2}}{\left(3-\sqrt{2}\right)\left(3+\sqrt{2}\right)}=\frac{3-\sqrt{2}}{7}\)
ND
14 tháng 7 2018
\(\dfrac{\sqrt{3}+\sqrt{4}+\sqrt{5}}{\sqrt{6}+\sqrt{8}+\sqrt{10}+\sqrt{27}+\sqrt{36}+\sqrt{45}}\)
\(=\dfrac{\sqrt{3}+\sqrt{4}+\sqrt{5}}{\sqrt{3}.\sqrt{2}+\sqrt{4}.\sqrt{2}+\sqrt{5}.\sqrt{2}+3\sqrt{3}+3\sqrt{4}+3\sqrt{5}}\)
\(=\dfrac{\sqrt{3}+\sqrt{4}+\sqrt{5}}{\sqrt{2}\left(\sqrt{3}+\sqrt{4}+\sqrt{5}\right)+3\left(\sqrt{3}+\sqrt{4}+\sqrt{5}\right)}\)
\(=\dfrac{\sqrt{3}+\sqrt{4}+\sqrt{5}}{\left(\sqrt{2}+3\right)\left(\sqrt{3}+\sqrt{4}+\sqrt{5}\right)}\)
\(=\dfrac{1}{\sqrt{2}+3}\)
21 tháng 6 2023
a: =2015+6-5=2016
b: =10căn 2+5căn 2-6căn 2=9căn 2
c: =3căn 3-4căn 3-5căn 3=-6căn 3
d: =2căn 3+3căn 3-4căn 3=căn 3
GH
21 tháng 6 2023
\(A=2015+6-5==2015+1=2016\)
\(B=5\sqrt{2^3}+\sqrt{5^2.2}-2\sqrt{3^2.2}\\ =10\sqrt{2}+5\sqrt{2}-6\sqrt{2}\\ =\left(10+5-6\right)\sqrt{2}=9\sqrt{2}\)
\(C=\sqrt{3^3}-2\sqrt{2^2.3}-\sqrt{5^2.3}\\ =3\sqrt{3}-4\sqrt{3}-5\sqrt{3}\\ =\left(3-4-5\right)\sqrt{3}=-6\sqrt{3}\)
\(D=\sqrt{2^2.3}+\sqrt{3^3}-\sqrt{4^2.3}\\ =2\sqrt{3}+3\sqrt{3}-4\sqrt{3}\\ =\left(2+3-4\right)\sqrt{3}=\sqrt{3}\)
NT
6 tháng 8 2021
a) \(2\sqrt{98}-3\sqrt{18}+\dfrac{1}{2}\sqrt{32}=14\sqrt{2}-9\sqrt{2}+2\sqrt{2}=7\sqrt{2}\)
b) \(\left(5\sqrt{2}+2\sqrt{5}\right).\sqrt{5}-\sqrt{250}=5\sqrt{10}+10-5\sqrt{10}=10\)
c) \(\left(2\sqrt{3}-5\sqrt{2}\right).\sqrt{3}-\sqrt{36}=6-5\sqrt{6}-6=5\sqrt{6}\)
d) \(3\sqrt{48}+2\sqrt{27}-\dfrac{1}{3}\sqrt{243}=12\sqrt{3}+6\sqrt{3}-3\sqrt{3}=15\sqrt{3}\)
e) \(6\sqrt{\dfrac{1}{3}}+\dfrac{9}{\sqrt{3}}-\dfrac{2}{\sqrt{3}-1}=2\sqrt{3}+3\sqrt{3}=\left(\sqrt{3}+1\right)=4\sqrt{3}-1\)
f) \(4\sqrt{\dfrac{1}{2}}-\dfrac{6}{\sqrt{2}}.\dfrac{2}{\sqrt{2}+1}=2\sqrt{2}-\left(12-6\sqrt{2}\right)=8\sqrt{2}-12\)
TN
1
2 tháng 11 2020
\(1,\left(\sqrt{45}-\sqrt{20}+\sqrt{5}\right):\sqrt{6}\)
\(=\left(\sqrt{9.5}\sqrt{4.5}+\sqrt{5}\right).\frac{1}{\sqrt{6}}\)
\(=\frac{2\sqrt{5}}{\sqrt{6}}\)
\(=\frac{\sqrt{30}}{3}\)
KV
3 tháng 11 2020
1) \(\left(\sqrt{45}-\sqrt{20}+\sqrt{5}\right):\sqrt{6}\)
\(=\left(\sqrt{9.5}-\sqrt{4.5}+\sqrt{5}\right):\sqrt{6}\)
\(=\left(3\sqrt{5}-2\sqrt{5}+\sqrt{5}\right):\sqrt{6}\)
\(=\frac{2\sqrt{5}}{\sqrt{6}}\)
\(=\frac{2\sqrt{5}\sqrt{6}}{\sqrt{6}.\sqrt{6}}\)
\(=\frac{2\sqrt{30}}{6}\)
\(=\frac{\sqrt{30}}{3}\)
13 tháng 11 2018
1
a,\(\sqrt{\dfrac{36}{121}}=\sqrt{\dfrac{6^2}{11^2}}=\dfrac{6}{11}\)
\(\sqrt{\dfrac{9}{16}:\dfrac{25}{36}}=\sqrt{\dfrac{81}{100}}=\sqrt{\dfrac{9^2}{10^2}}=\dfrac{9}{10}\)
\(\sqrt{3}-\sqrt{27}-\sqrt{144}:\sqrt{36}\)
\(=\sqrt{3}-\sqrt{27}-2\)
\(=-2\sqrt{3}-2\)
\(=-2-2\sqrt{3}\)
\(\sqrt{3}-\sqrt{27}-\sqrt{144}:\sqrt{36}\)
\(=\sqrt{3}-\sqrt{27}-\sqrt{4}\)
\(=\sqrt{3}-3\sqrt{3}-2\)
\(=-2-2\sqrt{3}\)