Viết những biểu thức sau dưới dạng bình phương của một tổng (hoặc hiệu)
a/\(34+24\sqrt{2}\)
b/\(69-28\sqrt{5}\)
c/\(2020-2\sqrt{2019}\)
K
Khách
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7 tháng 7 2021
b)\(27-10\sqrt{2}=5^2-2.5\sqrt{2}+2=\left(5-\sqrt{2}\right)^2\)
c)\(18-8\sqrt{2}=4^2-2.4\sqrt{2}+2=\left(4-\sqrt{2}\right)^2\)
d)\(4-2\sqrt{3}=3-2\sqrt{3}+1=\left(\sqrt{3}-1\right)^2\)
e)\(6\sqrt{5}+14=9+2.3\sqrt{5}+5=\left(3+\sqrt{5}\right)^2\)
f)\(20\sqrt{5}+45=5^2+2.5.2\sqrt{5}+20=\left(5+2\sqrt{5}\right)^2\)
g)\(7-2\sqrt{6}=6-2\sqrt{6}+1=\left(\sqrt{6}-1\right)^2\)
13 tháng 6 2015
a,\(5+\sqrt{24}=5+\sqrt{6.4}=5+2\sqrt{6}=\left(\sqrt{2}\right)^2+2\sqrt{2}\sqrt{3}+\left(\sqrt{3}\right)^2=\left(\sqrt{2}+\sqrt{3}\right)^2\)
b,\(14+6\sqrt{5}=14+2.3.\sqrt{5}=3^2+2.3\sqrt{5}+\left(\sqrt{5}\right)^2=\left(3+\sqrt{5}\right)^2\)
D
1
3 tháng 2 2022
b: \(5+2\sqrt{6}=\left(\sqrt{3}+\sqrt{2}\right)^2\)
c: \(13+\sqrt{48}=13+4\sqrt{3}=\left(2\sqrt{3}+1\right)^2\)
d: \(4+2\sqrt{3}=\left(\sqrt{3}+1\right)^2\)
N
3 tháng 9 2016
1) \(15-\sqrt{216}=15-\sqrt{4}.\sqrt{54}\)=\(9-2.\sqrt{9}.\sqrt{6}+6\)=\(\left(\sqrt{9}-\sqrt{6}\right)^2=\left(3-\sqrt{6}\right)^2\)
2)\(20-\sqrt{76}=20-\sqrt{4}.\sqrt{19}=19-2\sqrt{19}.1+1=\left(\sqrt{19}-1\right)^2\)
3)\(24-12\sqrt{3}=6\left(4-2\sqrt{3}\right)=6\left(3-2.\sqrt{3}.1+1\right)=6\left(\sqrt{3}-1\right)^2\)
4)\(7-\sqrt{13}=\frac{14-2\sqrt{13}}{2}=\frac{13-2\sqrt{13}.1+1}{2}=\frac{\left(\sqrt{13}-1\right)^2}{2}\)
5)\(16-\sqrt{31}=\frac{32-2\sqrt{31}}{2}=\frac{31-2\sqrt{31}.1+1}{2}=\frac{\left(\sqrt{31}-1\right)^2}{2}\)
12 tháng 6 2018
1)\(43-30\sqrt{2}=\left(5-3\sqrt{2}\right)^2\)
2)\(21+4\sqrt{5}=\left(1+2\sqrt{5}\right)^2\)
31 tháng 8 2017
1) \(5-2\sqrt{6}=\left(\sqrt{3}\right)^2-2\sqrt{3}.\sqrt{2}+\left(\sqrt{2}\right)^2=\left(\sqrt{3}-\sqrt{2}\right)^2\)
2) \(8+2\sqrt{15}=\left(\sqrt{5}\right)^2+2\sqrt{5}.\sqrt{3}+\left(\sqrt{3}\right)^2=\left(\sqrt{5}+\sqrt{3}\right)^2\)
3) \(10-2\sqrt{21}=\left(\sqrt{7}\right)^2-2\sqrt{7}.\sqrt{3}+\left(\sqrt{3}\right)^2=\left(\sqrt{7}-\sqrt{3}\right)^2\)
4) \(21+6\sqrt{6}=\left(\sqrt{18}\right)^2+2.\sqrt{18}.\sqrt{3}+\left(\sqrt{3}\right)^2=\left(\sqrt{18}+\sqrt{3}\right)^2\)
5) \(14+8\sqrt{3}=\left(\sqrt{8}\right)^2+2.\sqrt{8}.\sqrt{6}+\left(\sqrt{6}\right)^2=\left(\sqrt{8}+\sqrt{6}\right)^2\)
6) \(36-12\sqrt{5}=\left(\sqrt{30}\right)^2-2.\sqrt{30}.\sqrt{6}+\left(\sqrt{6}\right)^2=\left(\sqrt{30}-\sqrt{6}\right)^2\)
7) \(25+4\sqrt{6}=\left(\sqrt{24}\right)^2+2\sqrt{24}.1+1^2=\left(\sqrt{24}+1\right)^2\)
8) \(98-16\sqrt{3}=\left(\sqrt{96}\right)^2-2\sqrt{96}.\sqrt{2}+\left(\sqrt{2}\right)^2=\left(\sqrt{96}-\sqrt{2}\right)^2\)
2 tháng 9 2017
\(13-4\sqrt{3}=\left(2\sqrt{3}\right)^2-2.2\sqrt{2}.1+1^2=\left(2\sqrt{3}-1\right)^2\)
a) \(\left(\sqrt{5}+\sqrt{3}\right)\sqrt{8-2\sqrt{15}}=\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)=5-3=2\)
câu này \(\sqrt{15}\)đúng hơn \(\sqrt{5}\)
b) \(\sqrt{3-\sqrt{5}}-\sqrt{3+\sqrt{5}}=\frac{\sqrt{6-2\sqrt{5}}-\sqrt{6+2\sqrt{5}}}{\sqrt{2}}=\frac{\sqrt{5}-1-\sqrt{5}-1}{\sqrt{2}}=\frac{-2}{\sqrt{2}}=-\sqrt{2}\)c) \(\sqrt{5-2\sqrt{6}}-\sqrt{5+2\sqrt{6}}=\sqrt{3}-\sqrt{2}-\sqrt{3}-\sqrt{2}=-2\sqrt{2}\)
\(34+24\sqrt{2}=18+2\sqrt{288}+16=\left(\sqrt{18}\right)^2+2\sqrt{18}\cdot\sqrt{16}+\left(\sqrt{16}\right)^2=\left(\sqrt{18}+\sqrt{16}\right)^2\)