Rút gọn :
a) \(\sqrt{49-20\sqrt{6}}-\sqrt{106+20\sqrt{6}}\)
b) \(\sqrt{83-20\sqrt{6}}+\sqrt{62-20\sqrt{6}}\)
c) \(\sqrt{302-20\sqrt{6}}+\sqrt{203-20\sqrt{6}}\)
d) \(\sqrt{601-20\sqrt{6}}-\sqrt{154-20\sqrt{6}}\)
K
Khách
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Những câu hỏi liên quan
7 tháng 8 2022
\(A=\sqrt{47+\sqrt{5}}\cdot\sqrt{47-\sqrt{5}}\)
\(=\sqrt{2204}=2\sqrt{551}\)
\(B=5-2\sqrt{6}+10+\sqrt{6}=15-\sqrt{6}\)
7 tháng 8 2022
\(A=\sqrt{\left(47+\sqrt{5}\right)\left(47-\sqrt{5}\right)}=2\sqrt{551}\)
\(B=5-2\sqrt{6}+10+\sqrt{6}=15-\sqrt{6}\)
26 tháng 6 2015
B = \(\sqrt{\sqrt{75-2.2\sqrt{2}.5\sqrt{3}+8}+\sqrt{50-2.2\sqrt{3}.5\sqrt{2}+12}}.\sqrt{3\sqrt{3}-3\sqrt{2}}\)
= \(\sqrt{\sqrt{\left(5\sqrt{3}-2\sqrt{2}\right)^2}+\sqrt{\left(5\sqrt{2}+2\sqrt{3}\right)^2}}.\sqrt{3\sqrt{3}-3\sqrt{2}}\)
= \(\sqrt{5\sqrt{3}-2\sqrt{2}+5\sqrt{2}-2\sqrt{3}}.\sqrt{3\sqrt{3}-3\sqrt{2}}\)
= \(\sqrt{3\sqrt{3}+3\sqrt{2}}.\sqrt{3\sqrt{3}-3\sqrt{2}}=\sqrt{\left(3\sqrt{3}+3\sqrt{2}\right)\left(3\sqrt{3}-3\sqrt{2}\right)}\)
= \(\sqrt{27-18}=\sqrt{9}=3\)
CT
12 tháng 8 2019
Phân tích cái trong ngặc đầu thành: (5 căn 3 - 2 căn 2)^2
cái thứ 2 là ( 5 căn 2 - 2 căn 3)^2
sau đó phá đc 1 ngặc làm tiếp
NC
3
24 tháng 8 2023
\(\dfrac{1}{\sqrt{49+20\sqrt{6}}}-\dfrac{1}{\sqrt{49-20\sqrt{6}}}+\dfrac{1}{\sqrt{7-4\sqrt{3}}}\)
\(=\dfrac{1}{\sqrt{5^2+2\cdot2\sqrt{6}\cdot5+\left(2\sqrt{6}\right)^2}}-\dfrac{1}{\sqrt{5^2-2\cdot2\sqrt{6}\cdot5+\left(2\sqrt{6}\right)^2}}+\dfrac{1}{\sqrt{2^2-2\cdot2\cdot\sqrt{3}+\left(\sqrt{3}\right)^2}}\)
\(=\dfrac{1}{\sqrt{\left(5+2\sqrt{6}\right)^2}}-\dfrac{1}{\sqrt{\left(5-2\sqrt{6}\right)^2}}+\dfrac{1}{\sqrt{\left(2-\sqrt{3}\right)^2}}\)
\(=\dfrac{1}{5+2\sqrt{6}}-\dfrac{1}{5-2\sqrt{6}}+\dfrac{1}{2-\sqrt{3}}\)
\(=\dfrac{5-2\sqrt{6}}{\left(5+2\sqrt{6}\right)\left(5-2\sqrt{6}\right)}-\dfrac{5+2\sqrt{6}}{\left(5+2\sqrt{6}\right)\left(5-2\sqrt{6}\right)}+\dfrac{2+\sqrt{3}}{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}\)
\(=\dfrac{5-2\sqrt{6}-5-2\sqrt{6}}{1}+\dfrac{2+\sqrt{3}}{1}\)
\(=-4\sqrt{6}+2+\sqrt{3}\)
24 tháng 8 2023
\(=\dfrac{1}{5+2\sqrt{6}}-\dfrac{1}{5-2\sqrt{6}}+\dfrac{1}{2-\sqrt{3}}\)
\(=5-2\sqrt{6}-5-2\sqrt{6}+2+\sqrt{3}\)
\(=2-4\sqrt{6}+\sqrt{3}\)
2
24 tháng 9 2023
`a)(\sqrt{14}-3\sqrt{2})^2+6\sqrt{28}`
`=14-12\sqrt{7}+18+12\sqrt{7}=32`
`b)2\sqrt{20}-3\sqrt{20}+\sqrt{125}`
`=4\sqrt{5}-6\sqrt{5}+5\sqrt{5}`
`=3\sqrt{5}`.
24 tháng 9 2023
a) \(\left(\sqrt{14}-3\sqrt{2}\right)^2-6\sqrt{28}\)
\(=\left(\sqrt{14}\right)^2-2\cdot\sqrt{14}\cdot3\sqrt{2}+\left(3\sqrt{2}\right)^2+6\sqrt{28}\)
\(=14-6\sqrt{28}+18+6\sqrt{28}\)
\(=14+18\)
\(=32\)
b) \(2\sqrt{20}-3\sqrt{20}+\sqrt{125}\)
\(=2\cdot2\sqrt{5}-3\cdot2\sqrt{5}+5\sqrt{5}\)
\(=4\sqrt{5}-6\sqrt{5}+5\sqrt{5}\)
\(=3\sqrt{5}\)
5 tháng 5 2016
Ta có \(\sqrt[4]{49+20\sqrt{6}}=\sqrt[4]{25+10\sqrt{24}+24}=\sqrt[4]{\left(5+2\sqrt{6}\right)^2}\)
\(=\sqrt[4]{\left(\sqrt{3}+\sqrt{2}\right)^4}=\sqrt{3}+\sqrt{2}\)
Tương tự : \(\sqrt[4]{49-20\sqrt{6}}=\sqrt{3}-\sqrt{2}\) ( Do \(\sqrt{3}>\sqrt{2}\) )
Suy ra \(\sqrt[4]{49+20\sqrt{6}}+\sqrt[4]{49-20\sqrt{6}}=2\sqrt{3}\)
NV
Nguyễn Việt Lâm
Giáo viên
6 tháng 7 2021
\(A=\dfrac{\sqrt{\left(\sqrt{5}+1\right)^2}-\sqrt{2}.\sqrt{6-2\sqrt{5}}+\sqrt{\left(\sqrt{10}-\sqrt{5}\right)^2}}{2\left(\sqrt{2}+1\right)}\)
\(=\dfrac{\sqrt{5}+1-\sqrt{2}\left(\sqrt{5}-1\right)+\sqrt{10}-\sqrt{5}}{2\left(\sqrt{2}+1\right)}\)
\(=\dfrac{\sqrt{5}+1-\sqrt{10}+\sqrt{2}+\sqrt{10}-\sqrt{5}}{2\left(\sqrt{2}+1\right)}\)
\(=\dfrac{\sqrt{2}+1}{2\left(\sqrt{2}+1\right)}=\dfrac{1}{2}\)
a. \(\sqrt{49-20\sqrt{6}}-\sqrt{106+20\sqrt{6}}=\sqrt{\left(5-2\sqrt{6}\right)^2}-\sqrt{\left(10+\sqrt{6}\right)^2}=5-2\sqrt{6}-10-\sqrt{6}=-5-3\sqrt{6}\)
b. \(\sqrt{83-20\sqrt{6}}+\sqrt{62-20\sqrt{6}}=\sqrt{\left(5\sqrt{3}-2\sqrt{2}\right)^2}+\sqrt{\left(5\sqrt{2}-2\sqrt{3}\right)^2}=5\sqrt{3}-2\sqrt{2}+5\sqrt{2}-2\sqrt{3}=3\sqrt{3}+3\sqrt{2}\)
c. \(\sqrt{302-20\sqrt{6}}+\sqrt{203-20\sqrt{6}}=\sqrt{\left(10\sqrt{3}-\sqrt{2}\right)^2}+\sqrt{\left(10\sqrt{2}-\sqrt{3}\right)^2}=10\sqrt{3}-\sqrt{2}+10\sqrt{2}-\sqrt{3}=9\sqrt{3}+9\sqrt{2}\)
d. \(\sqrt{601-20\sqrt{6}}-\sqrt{154-20\sqrt{6}}=\sqrt{\left(10\sqrt{6}-1\right)^2}-\sqrt{\left(5\sqrt{6}-2\right)^2}=10\sqrt{6}-1-5\sqrt{6}+2=1+5\sqrt{6}\)