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TT
1
25 tháng 6 2020
a) \(\sqrt{6,8^2-3.2^2}\)
\(=\sqrt{\left(6,8+3,2\right).\left(6,8-3,2\right)}\)
\(=\sqrt{3,6.10}=\sqrt{36}=6\)
b) \(\sqrt{21,8^2-18,2^2}\)
\(=\sqrt{\left(21,8-18,2\right).\left(21,8+18,2\right)}\)
\(=\sqrt{3,6.40}=\sqrt{4.36}=2.6=12\)
Y
4 tháng 7 2023
\(a,\dfrac{1}{2-\sqrt{3}}-3\sqrt{\dfrac{1}{3}}+\sqrt{12}\\ =\dfrac{2+\sqrt{3}}{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}-\dfrac{\sqrt{3^2}}{\sqrt{3}}+\sqrt{2^2.3}\\ =\dfrac{2+\sqrt{3}}{4-3}-\sqrt{3}+2\sqrt{3}\\ =2+\sqrt{3}-\sqrt{3}+2\sqrt{3}\\ =2+2\sqrt{3}\)
\(b,\dfrac{2}{1+\sqrt{2}}-\sqrt{9-\sqrt{32}}\\ =\dfrac{2\left(1-\sqrt{2}\right)}{\left(1+\sqrt{2}\right)\left(1-\sqrt{2}\right)}-\sqrt{9-4\sqrt{2}}\\ =\dfrac{2-2\sqrt{2}}{1-2}-\sqrt{\left(2\sqrt{2}\right)^2-2.2\sqrt{2}+1}\\ =-2+2\sqrt{2}-\sqrt{\left(2\sqrt{2}-1\right)^2}\\ =-2+2\sqrt{2}-\left|2\sqrt{2}-1\right|\\ =-2+2\sqrt{2}-2\sqrt{2}+1\\ =-1\)
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: \(C=4\sqrt{2}-5\sqrt{2}+3\sqrt{2}=2\sqrt{2}\)
29 tháng 8 2021
Bài 1:
a: \(\sqrt{252}-\sqrt{700}+\sqrt{1008}-\sqrt{448}\)
\(=6\sqrt{7}-10\sqrt{7}+12\sqrt{7}-8\sqrt{7}\)
\(=8\sqrt{7}\)
30 tháng 8 2021
Bài 3:
a: \(\sqrt{27^2-23^2}=10\sqrt{2}\)
b: \(\sqrt{37^2-35^2}=12\)
c: \(\sqrt{65^2-63^2}=16\)
d: \(\sqrt{117^2-108^2}=45\)
LT
6 tháng 7 2016
\(\frac{\sqrt{12,5}}{\sqrt{0,5}}=\frac{\sqrt{0,5}.\sqrt{25}}{\sqrt{0,5}}=\sqrt{25}=5\)
\(\frac{\sqrt{6}}{\sqrt{150}}=\frac{\sqrt{6}}{\sqrt{6}.\sqrt{25}}=\frac{1}{\sqrt{25}}=\frac{1}{5}\)
\(\sqrt{6,8^2-3,2^2}=\sqrt{\left(6,8+3,2\right)\left(6,8-3,2\right)}=\sqrt{10.3,6}=\sqrt{36}=6\)
\(\sqrt{21,8^2-18,2^2}=\sqrt{\left(21,8+18,2\right)\left(21,8-18,2\right)}=\sqrt{40.3,6}=\sqrt{144}=12\)
6 tháng 7 2016
\(\frac{\sqrt{12,5}}{\sqrt{0,5}}=\sqrt{\frac{12,5}{0,5}}=\sqrt{25}=5\)
\(\frac{\sqrt{6}}{\sqrt{150}}=\sqrt{\frac{6}{150}}=\sqrt{\frac{1}{25}}=\frac{1}{5}\)
\(\sqrt{\left(6,8\right)^2-\left(3,2\right)^2}=\sqrt{46,24-10,24}=\sqrt{36}=6\)
\(\sqrt{\left(21,8\right)^2-\left(18,2\right)^2}=\sqrt{475,24-331,24}=\sqrt{144}=12\)
18 tháng 7 2017
\(a=\sqrt{\left(6,8-3,2\right)\left(6,8+3,2\right)}=\sqrt{3,6\left(10\right)}=\sqrt{36}=6\)
LD
21 tháng 9 2017
a) \(\sqrt{6,8^2-3,2^2}=\sqrt{\left(6,8-3,2\right)\left(6,8+3,2\right)}\)
=\(\sqrt{3,6.10}=\sqrt{36}=6\)
b)\(\sqrt{21,8^2-18,2^2}=\sqrt{\left(21,8-18,2\right)\left(21,8+18,2\right)}\)
=\(\sqrt{3,6.40}=\sqrt{144}=12\)
c)\(\sqrt{117,5^2-26,5^2-1440}=\sqrt{\left(117,5-26,5\right)\left(117,5+26,5\right)-1440}\)
=\(\sqrt{91.144-1440}=\sqrt{144.81}=\sqrt{144}.\sqrt{81}=108\)
d)\(\sqrt{146,5^2-109,5^2+27.256}\)=\(\sqrt{\left(146,5-109,5\right)\left(146,5+109,5\right)+27.256}\)
=\(\sqrt{37.256+\sqrt{27.256}}=\sqrt{64.256}=\sqrt{64}.\sqrt{256}=128\)
HP
3 tháng 9 2021
b, \(\dfrac{2}{\sqrt{5}+2}+\dfrac{2}{2-\sqrt{5}}\)
\(=\dfrac{2\left(\sqrt{5}-2\right)}{5-4}-\dfrac{2\left(\sqrt{5}+2\right)}{5-4}\)
\(=2\sqrt{5}-4-2\sqrt{5}-4=-8\)
11 tháng 9 2019
1,
\(a,=\sqrt{\left(21,8-18,2\right)\left(21,8+18,2\right)}\\ =\sqrt{3,6\cdot40}\\ =\sqrt{36\cdot4}\\ =\sqrt{36}\cdot\sqrt{4}\\ =6\cdot4\\ =24\)
\(b,=10\cdot\sqrt{\left(6,5-1,6\right)\left(6,5+1,6\right)}\\ =10\cdot\sqrt{4,9\cdot8,1}\\ =10\cdot\sqrt{49\cdot0,81}\\ =10\cdot\sqrt{49}\cdot\sqrt{0,81}\\ =10\cdot7\cdot0,9\\ =63\)
2,
\(A=7+4\sqrt{3}+\sqrt{3}-1\\ =6+5\sqrt{3}\\ B=7+2\sqrt{10}-\left(11+2\sqrt{10}\right)\\ =7+2\sqrt{10}-11-2\sqrt{10}\\ =-4\)
TN
1
19 tháng 8 2021
\(a,8+2\sqrt{15}=\left(\sqrt{3}+\sqrt{5}\right)^2\\ b,12+2\sqrt{35}=\left(\sqrt{7}+\sqrt{5}\right)^2\\ c,8+\sqrt{60}=8+2\sqrt{15}=\left(\sqrt{3}+\sqrt{5}\right)^2\)
\(a,\sqrt{68^2-32^2}\)
\(=\sqrt{\left(68-32\right)\left(68+32\right)}\)
\(=\sqrt{3600}=60\)
\(b,\sqrt{37^2-12^2}\)
\(=\sqrt{\left(37-12\right)\left(37+12\right)}\)
\(=\sqrt{25.49}=5.7=35\)
\(c,\sqrt{21,8^2-18,2^2}\)
\(=\sqrt{\left(21,8+18,2\right)\left(21,8-18,2\right)}\)
\(=\sqrt{40.3,6}=12\)