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1) \(=\sqrt{\left(\sqrt{3}-1\right)^2}=\sqrt{3}-1\)
2) \(=\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}=\sqrt{3}+\sqrt{2}\)
3) \(=\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}=\sqrt{5}-\sqrt{2}\)
5) \(=\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}=\sqrt{5}+\sqrt{3}\)
6) \(=\sqrt{\left(\sqrt{7}-\sqrt{3}\right)^2}=\sqrt{7}-\sqrt{3}\)
7) \(=\sqrt{\left(3+\sqrt{2}\right)^2}=3+\sqrt{2}\)
1/ \(7-2\sqrt{6}=\left(\sqrt{6}\right)^2-2\sqrt{6}+1\)
\(=\left(\sqrt{6}-1\right)^2\)
2/ \(10+2\sqrt{21}=\left(\sqrt{7}\right)^2+2.\sqrt{7}.\sqrt{3}+\left(\sqrt{3}\right)^2\)
\(=\left(\sqrt{7}+\sqrt{3}\right)^2\)
4/ \(10+4\sqrt{6}=2^2+2.2.\sqrt{6}+\left(\sqrt{6}\right)^2\)
\(=\left(2+\sqrt{6}\right)^2\)
5/ \(11-2\sqrt{30}=\left(\sqrt{6}\right)^2-2.\sqrt{6}.\sqrt{5}+\left(\sqrt{5}\right)^2\)
= \(\left(\sqrt{6}-\sqrt{5}\right)^2\)
8/ \(11+4\sqrt{7}=2^2+2.2.\sqrt{7}+\left(\sqrt{7}\right)^2\)
= \(\left(2+\sqrt{7}\right)^2\)
10/ \(12+6\sqrt{3}=3^2+2.3.\sqrt{3}+\left(\sqrt{3}\right)^2\)
= \(\left(3+\sqrt{3}\right)^2\)
A = ((20 + 1) . 20 : 2) . 2 = 420
B = (25 + 20) . 6 : 2 = 135
C = ( 33 + 26) . 8 : 2 = 236
D = (1 + 100) .100 : 2 = 5050
81 ; 11660 ; 2 ; 4 ; 6 ; 8 ; 10 ; 12 ; 14 ; 16 ; 18 ; 20 ; 34 ; 42 .
1)
\(=\sqrt{\left(\sqrt{11}\right)^2-2.\sqrt{11}.\sqrt{3}+\left(\sqrt{3}\right)^2}\)
\(=\sqrt{\left(\sqrt{11}-\sqrt{3}\right)^2}=\sqrt{11}-\sqrt{3}\)
2)
\(=\sqrt{\left(\sqrt{7}\right)^2-2.\sqrt{7}\sqrt{5}+\left(\sqrt{5}\right)^2}=\sqrt{\left(\sqrt{7}-\sqrt{5}\right)^2}=\sqrt{7}-\sqrt{5}\)
3)
\(=\sqrt{\left(\sqrt{11}\right)^2-2.\sqrt{11}\sqrt{5}+\left(\sqrt{5}\right)^2}=\sqrt{\left(\sqrt{11}-\sqrt{5}\right)}=\sqrt{11}-\sqrt{5}\)
4)
\(=\sqrt{3^2-2.3.\sqrt{5}+\left(\sqrt{5}\right)^2}=\sqrt{\left(3-\sqrt{5}\right)^2}=3-\sqrt{5}\)
5)
\(=\sqrt{3^2-2.3.2\sqrt{2}+\left(2\sqrt{2}\right)^2}=\sqrt{\left(3-2\sqrt{2}\right)^2}=3-2\sqrt{2}\)
nếu tính đầy đủ thì = 19 + 1 , 18 + 2 , 17 + 3 , 16 + 4 , 15 + 5 , 14 + 6 , 13 + 7 , 12 + 8 , 11 + 9 = 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 20 + 20 + 20 + 20 + 20 + 20 + 20 + 20 + 20 = 40 + 40 + 40 + 40 + 20 = 180 nếu tính tắt thì : 20 x 9 = 180
Ta lấy (1+19)+(2+18)+....(9+11) + 10 + 20
vì 1+19 = 20
mà từ 1 - 19 ( bỏ số 10 ra vì nó chẵn ) có tất cả là 9 cặp
=> 20*9=180 + 10+20 = 210
tk minh nha
14) \(\sqrt{7-4\sqrt{3}}=2-\sqrt{3}\)
15) \(\sqrt{8+2\sqrt{15}}=\sqrt{5}+\sqrt{3}\)
16) \(\sqrt{10-2\sqrt{21}}=\sqrt{7}-\sqrt{3}\)
17) \(\sqrt{11+2\sqrt{18}}=3+\sqrt{2}\)
18) \(\sqrt{7+2\sqrt{10}}=\sqrt{5}+\sqrt{2}\)
19) \(\sqrt{7+4\sqrt{3}}=2+\sqrt{3}\)
20) \(\sqrt{12-2\sqrt{35}}=\sqrt{7}-\sqrt{5}\)
`sqrt{5+2sqrt6}`
`=sqrt{3+2sqrt3sqrt2+2}`
`=sqrt{(sqrt3+sqrt2)^2}`
`=|sqrt3+sqrt2|=sqrt3+sqrt2`
`7. sqrt(4+2sqrt3)`
`=sqrt{3+2sqrt3+1}`
`=sqrt{(sqrt3+1)^2}`
`=sqrt3+1`
`8. sqrt(4-2sqrt3)`
`=sqrt{3-2sqrt3+1}`
`=sqrt{(sqrt3-1)^2}`
`=sqrt3-1`
`9. sqrt(11-2sqrt(30))`
`=sqrt{6-2sqrt5sqrt6+5}`
`=sqrt{(sqrt6-sqrt5)^2}`
`=sqrt6-sqrt5`
`10. sqrt(21-4sqrt(17))`
`=sqrt{17-2.2.sqrt{17}+4}`
`=sqrt{(sqrt{17}-2)^2}`
`=sqrt{17}-2`
1, \(\sqrt{5+2\sqrt{6}}\)=\(\sqrt{2+2\sqrt{6}+3}\) =\(\sqrt{\left(\sqrt{2}+\sqrt{3}\right)^2}\)=\(\sqrt{2}+\sqrt{3}\)
2,\(\sqrt{11+2\sqrt{30}}\)=\(\sqrt{5+2\sqrt{30}+6}\)=\(\sqrt{\left(\sqrt{5}+\sqrt{6}\right)^2}\)=\(\sqrt{5}+\sqrt{6}\)
3, \(\sqrt{8-2\sqrt{15}}\)=\(\sqrt{5-2\sqrt{15}+3}\)=\(\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}\)=\(\sqrt{5}-\sqrt{3}\)
4,\(\sqrt{7-4\sqrt{3}}\)=\(\sqrt{4-4\sqrt{3}+3}\)=\(\sqrt{\left(2-\sqrt{3}\right)^2}\)=\(2-\sqrt{3}\)
5,\(\sqrt{12-2\sqrt{35}}\)=\(\sqrt{7-2\sqrt{35}+5}=\sqrt{\left(\sqrt{7}-\sqrt{5}\right)^2}\) =\(\sqrt{7}-\sqrt{5}\)
6,\(\sqrt{14-6\sqrt{5}}=\sqrt{9-6\sqrt{5}+5}=\sqrt{\left(3-\sqrt{5}\right)^2}=3-\sqrt{5}\)
Mình chỉ làm đc tới đây thui sorry bn nha