\(\sqrt{5}\)+ \(\sqrt{500}\)+ \(\sqrt{720}\)
\(\sqrt{8}\)+ \(\sqrt{32}\)+ \(\sqrt{50}\)
\(\sqrt{72}\)+ \(\sqrt{8}\)+\(\sqrt{18}\)
K
Khách
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24 tháng 10 2021
c: Ta có: \(C=\left(\dfrac{\sqrt{3}+1}{\sqrt{3}-1}-\dfrac{\sqrt{3}-1}{\sqrt{3}+1}\right):\sqrt{48}\)
\(=\dfrac{4+2\sqrt{3}-4+2\sqrt{3}}{2}:4\sqrt{3}\)
\(=\dfrac{1}{2}\)
KV
8 tháng 11 2023
a) 2√18 - 4√50 + 3√32
= 6√2 - 20√2 + 12√2
= -2√2
b) √(√8 - 4)² + √8
= 4 - √8 + √8
= 4
c) √(14 - 6√5) + √(6 + 2√5)
= √(3 - √5)² + √(√5 + 1)²
= 3 - √5 + √5 + 1
= 4
TA
8 tháng 11 2023
\(a,2\sqrt{18}-4\sqrt{50}+3\sqrt{32}\\ =6\sqrt{2}-20\sqrt{2}+12\sqrt{2}=-2\sqrt{2}\\ b,\sqrt{\left(\sqrt{8}-4\right)^2}+\sqrt{8}\\ =4-\sqrt{8}+\sqrt{8}\\ =4\\ c,\sqrt{14-6\sqrt{5}}+\sqrt{6+2\sqrt{5}}\\ =\sqrt{\left(3+\sqrt{5}\right)^2}+\sqrt{\left(\sqrt{5}+1\right)^2}=3+\sqrt{5}+\sqrt{5}+1\\ =4+2\sqrt{5}\)
22 tháng 8 2021
a: Ta có: \(\sqrt{8+2\sqrt{15}}-\sqrt{6+2\sqrt{5}}\)
\(=\sqrt{5}+\sqrt{3}-\sqrt{5}-1\)
\(=\sqrt{3}-1\)
b: Ta có: \(\sqrt{17-2\sqrt{72}}+\sqrt{19+2\sqrt{18}}\)
\(=3-2\sqrt{2}+3\sqrt{2}+1\)
\(=4+\sqrt{2}\)
c: Ta có: \(\sqrt{12-2\sqrt{32}}+\sqrt{9+4\sqrt{2}}\)
\(=2\sqrt{2}-2+2\sqrt{2}+1\)
\(=4\sqrt{2}-1\)
22 tháng 8 2021
a)
\(\sqrt{8+2\sqrt{15}}-\sqrt{6+2\sqrt{5}}\\ =\sqrt{5+2\sqrt{5}\cdot\sqrt{3}+3}-\sqrt{5+2\sqrt{5}\cdot\sqrt{1}+1}\\ =\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}-\sqrt{\left(\sqrt{5}+\sqrt{1}\right)^2}\\ =\sqrt{5}+\sqrt{3}-\sqrt{5}-\sqrt{1}\\ =\sqrt{3}-\sqrt{1}\)
b)
\(\sqrt{17-2\sqrt{72}}+\sqrt{19+2\sqrt{18}}\\ =\sqrt{9-2\sqrt{9}\cdot\sqrt{8}+8}+\sqrt{18+2\sqrt{18}\cdot\sqrt{1}+1}\\ =\sqrt{\left(3-2\sqrt{2}\right)^2}+\sqrt{\left(3\sqrt{2}+1\right)^2}\\ =3-2\sqrt{2}+3\sqrt{2}+1\\ =4+\sqrt{2}\)
c)
\(\sqrt{12-2\sqrt{32}}+\sqrt{9+4\sqrt{2}}\\ =\sqrt{8-2\sqrt{8}\cdot\sqrt{4}+4}+\sqrt{8+2\sqrt{8}\cdot\sqrt{1}+1}\\ =\sqrt{\left(2\sqrt{2}-2\right)^2}+\sqrt{\left(2\sqrt{2}+1\right)^2}\\ =2\sqrt{2}-2+2\sqrt{2}+1\\ =4\sqrt{2}-1\)
D
1
15 tháng 12 2022
\(=5\sqrt{2}-\dfrac{3}{2}\cdot4\sqrt{2}-\dfrac{1}{3}\cdot6\sqrt{2}+8=-3\sqrt{2}+8\)
13 tháng 5 2022
a: \(A=\left(1-\sqrt{7}\right)\cdot\left(1+\sqrt{7}\right)=1-7=-6\)
b: \(B=3\sqrt{3}+8\sqrt{3}-15\sqrt{3}=-4\sqrt{3}\)
c: \(C=4\sqrt{2}-5\sqrt{2}+3\sqrt{2}=2\sqrt{2}\)
10 tháng 6 2018
B=\(2\sqrt{18}-4\sqrt{32}+\sqrt{72}+3\sqrt{8}\)
\(=6\sqrt{2}-16\sqrt{2}+6\sqrt{2}+6\sqrt{2}\)
\(=2\sqrt{2}\)
TV
11 tháng 6 2018
\(B=2\sqrt{18}-4\sqrt{32}+\sqrt{72}+3\sqrt{8}\)
\(=6\sqrt{2}-16\sqrt{2}+6\sqrt{2}+6\sqrt{2}\)
\(=\sqrt{2}\left(6-16+6+6\right)\)
\(=2\sqrt{2}\)
LM
1 tháng 8 2018
1, \(\sqrt{8}-3\sqrt{32}+\sqrt{72}=2\sqrt{2}-12\sqrt{2}+6\sqrt{2}=-4\sqrt{2}\)
2,\(6\sqrt{12}-2\sqrt{48}+5\sqrt{75}-7\sqrt{108}=12\sqrt{3}-8\sqrt{3}+25\sqrt{3}-42\sqrt{3}=-13\sqrt{3}\)
3, \(\sqrt{20}+3\sqrt{45}-6\sqrt{80}-\dfrac{1}{3}\sqrt{125}=2\sqrt{5}+9\sqrt{5}-24\sqrt{5}-\dfrac{5}{3}.\sqrt{5}=-\dfrac{44}{3}.\sqrt{5}\)
4, \(2\sqrt{5}-\sqrt{125}-\sqrt{80}=2\sqrt{5}-5\sqrt{5}-4\sqrt{5}=-7\sqrt{5}\)
5, \(3\sqrt{2}-\sqrt{8}+\sqrt{50}-4\sqrt{32}=3\sqrt{2}-2\sqrt{2}+5\sqrt{2}-16\sqrt{2}=-10\sqrt{2}\)
6 tháng 7 2018
\(C=\sqrt{\sqrt{\left(5+2\right)^2}}-\sqrt{5}\\ =\sqrt{5+2}-\sqrt{5}=\sqrt{7}-\sqrt{5}\)
\(D=\sqrt{8}+\sqrt{18}-\sqrt{32}\\ =\sqrt{2}\left(\sqrt{4}+\sqrt{9}-\sqrt{16}\right)\\ =\sqrt{2}\left(2+3-4\right)\\ =\sqrt{2}\)
\(E=\sqrt{9-4\sqrt{5}}-\sqrt{5}\\ =\sqrt{4+5-4\sqrt{5}}-\sqrt{5}\\ =\sqrt{\left(\sqrt{5}-2\right)^2}-\sqrt{5}\\ =\sqrt{5}-2-\sqrt{5}\\ =-2\)
\(F=2\sqrt{8}-\sqrt{50}+\sqrt{\left(\sqrt{2}+1\right)^2}\\ =2\sqrt{8}-\sqrt{50}+\sqrt{2}+1\\ =\sqrt{2}\left(2\sqrt{4}-\sqrt{25}+1\right)+1\\ =\sqrt{2}\left(4-5+1\right)+1=1\)
H9
HT.Phong (9A5)
CTVHS
12 tháng 8 2023
a) \(\sqrt{200}-\sqrt{32}+\sqrt{72}\)
\(=\sqrt{10^2\cdot2}-\sqrt{4^2\cdot2}+\sqrt{6^2\cdot2}\)
\(=10\sqrt{2}-4\sqrt{2}+6\sqrt{2}\)
\(=\left(10-4+6\right)\sqrt{2}\)
\(=12\sqrt{2}\)
b) \(4\sqrt{20}-3\sqrt{125}+5\sqrt{45}-15\sqrt{\dfrac{1}{5}}\)
\(=4\cdot2\sqrt{5}-3\cdot5\sqrt{5}+5\cdot3\sqrt{5}-3\sqrt{5}\)
\(=8\sqrt{5}-15\sqrt{5}+15\sqrt{5}-3\sqrt{5}\)
\(=\left(8-15+15-3\right)\sqrt{5}\)
\(=5\sqrt{5}\)
c) \(\left(2\sqrt{8}+3\sqrt{5}-7\sqrt{2}\right)\left(72-5\sqrt{20}-2\sqrt{2}\right)\)
\(=\left(2\cdot2\sqrt{2}+3\sqrt{5}-7\sqrt{2}\right)\left(72-5\cdot2\sqrt{5}-2\sqrt{2}\right)\)
\(=\left(3\sqrt{5}-3\sqrt{2}\right)\left(72-10\sqrt{5}-2\sqrt{2}\right)\)
