Bài 1: Căn bậc hai
Các câu hỏi tương tự
Bài 1:
1.\(\sqrt{2-\sqrt{3}}\)
2.\(\sqrt{3+\sqrt{5}}\)
3.\(\sqrt{21-6\sqrt{6}}\)
4.\(\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}\)
5.\(\left(2-\sqrt{3}\right)\sqrt{7+4\sqrt{3}}\)
6.\(\sqrt{13+4\sqrt{10}}+\sqrt{13-4\sqrt{10}}\)
Tính:
a) dfrac{sqrt{7}-5}{2}-dfrac{6-2sqrt{7}}{4}+dfrac{6}{sqrt{7}-2}-dfrac{5}{4+sqrt{7}}
b) dfrac{2}{sqrt{6}-2}+dfrac{2}{sqrt{6}+2}+dfrac{5}{sqrt{6}}
c) dfrac{1}{sqrt{3}}+dfrac{1}{3sqrt{2}}+dfrac{1}{sqrt{3}}sqrt{dfrac{5}{12}-dfrac{1}{sqrt{6}}}
d) dfrac{2sqrt{3-sqrt{3+sqrt{13+sqrt{48}}}}}{sqrt{6}-sqrt{2}}
Đọc tiếp
Tính:
a) \(\dfrac{\sqrt{7}-5}{2}-\dfrac{6-2\sqrt{7}}{4}+\dfrac{6}{\sqrt{7}-2}-\dfrac{5}{4+\sqrt{7}}\)
b) \(\dfrac{2}{\sqrt{6}-2}+\dfrac{2}{\sqrt{6}+2}+\dfrac{5}{\sqrt{6}}\)
c) \(\dfrac{1}{\sqrt{3}}+\dfrac{1}{3\sqrt{2}}+\dfrac{1}{\sqrt{3}}\sqrt{\dfrac{5}{12}-\dfrac{1}{\sqrt{6}}}\)
d) \(\dfrac{2\sqrt{3-\sqrt{3+\sqrt{13+\sqrt{48}}}}}{\sqrt{6}-\sqrt{2}}\)
a) \(\sqrt{13-4\sqrt{3}}+\sqrt{7-4\sqrt{3}}\)
b) \(\sqrt{6+2\sqrt{5}}+\sqrt{6-2\sqrt{5}}\)
c) \(\sqrt{4+2\sqrt{3}}-\sqrt{4-2\sqrt{3}}\)
d) \(\sqrt{7+4\sqrt{3}}+\sqrt{7-4\sqrt{3}}\)
e) \(\sqrt{9+4\sqrt{5}}\)
f) \(\sqrt{23+8\sqrt{7}}\)
Bài 2
a) A sqrt{left(1-sqrt{2}right)^2}+sqrt{left(-2right)^6}-sqrt{left(1+sqrt{2}right)^2}
b) B sqrt{7+2sqrt{6}}+sqrt{7-2sqrt{6}}
c) C sqrt{7-4sqrt{3}}
d) D 2sqrt{7+4sqrt{3}}-sqrt{13-4sqrt{3}}
e) E frac{1}{1+sqrt{3}}+frac{1}{sqrt{3}+sqrt{5}}+...+frac{1}{sqrt{79}+sqrt{81}}
Bài 4:
a) sqrt{x-1}2
b) sqrt{x^2-3x+2}sqrt{2}
c) sqrt{4x+1}x+1
d) sqrt{x+2sqrt{x-1}}-sqrt{x-2sqrt{x-1}}2
e) sqrt{x^2-4x+5}+sqrt{x^2-4x+8}+sqrt{x^2-4x+9}3+sqrt{5}
f)
Đọc tiếp
Bài 2
a) A= \(\sqrt{\left(1-\sqrt{2}\right)^2}+\sqrt{\left(-2\right)^6}-\sqrt{\left(1+\sqrt{2}\right)^2}\)
b) B= \(\sqrt{7+2\sqrt{6}}+\sqrt{7-2\sqrt{6}}\)
c) C= \(\sqrt{7-4\sqrt{3}}\)
d) D= \(2\sqrt{7+4\sqrt{3}}-\sqrt{13-4\sqrt{3}}\)
e) E= \(\frac{1}{1+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{5}}+...+\frac{1}{\sqrt{79}+\sqrt{81}}\)
Bài 4:
a) \(\sqrt{x-1}=2\)
b) \(\sqrt{x^2-3x+2}=\sqrt{2}\)
c) \(\sqrt{4x+1}=x+1\)
d) \(\sqrt{x+2\sqrt{x-1}}-\sqrt{x-2\sqrt{x-1}}=2\)
e) \(\sqrt{x^2-4x+5}+\sqrt{x^2-4x+8}+\sqrt{x^2-4x+9}=3+\sqrt{5}\)
f)
Bài 1: viết thành căn bậc hai
1) 3-2√2
2) 8+2√7
3) x-2√x-1
4) 6-4√2
5) 7+4√3
6) 9-4√5
7) 10+2√21
8) 49+20√6
Asqrt{19-3sqrt{ }40}-sqrt{19+3sqrt{ }40}
Bsqrt{21-6sqrt{ }6} +sqrt{9+2sqrt{ }18} -2sqrt{6+3sqrt{ }3}
Csqrt{6+2sqrt{ }2sqrt{ }3-sqrt{ }4+2sqrt{ }3}
Dsqrt{4+sqrt{ }15}-sqrt{7-3sqrt{ }5}
Esqrt{2+sqrt{ }3}+sqrt{2-sqrt{ }3}
Fsqrt{12-3sqrt{ }7}-sqrt{12+3sqrt{ }7}
G(3sqrt{2}+sqrt{6}).sqrt{6-3sqrt{ }3}
Hsqrt{9-4sqrt{ }5}-sqrt{14-6sqrt{ }5}
Isqrt{9-4sqrt{ }2}-sqrt{13-4sqrt{ }3}
Đọc tiếp
A=\(\sqrt{19-3\sqrt{ }40}\)-\(\sqrt{19+3\sqrt{ }40}\)
B=\(\sqrt{21-6\sqrt{ }6}\) +\(\sqrt{9+2\sqrt{ }18}\) -2\(\sqrt{6+3\sqrt{ }3}\)
C=\(\sqrt{6+2\sqrt{ }2\sqrt{ }3-\sqrt{ }4+2\sqrt{ }3}\)
D=\(\sqrt{4+\sqrt{ }15}\)-\(\sqrt{7-3\sqrt{ }5}\)
E=\(\sqrt{2+\sqrt{ }3}\)+\(\sqrt{2-\sqrt{ }3}\)
F=\(\sqrt{12-3\sqrt{ }7}\)-\(\sqrt{12+3\sqrt{ }7}\)
G=(3\(\sqrt{2}\)+\(\sqrt{6}\)).\(\sqrt{6-3\sqrt{ }3}\)
H=\(\sqrt{9-4\sqrt{ }5}-\sqrt{14-6\sqrt{ }5}\)
I=\(\sqrt{9-4\sqrt{ }2}\)-\(\sqrt{13-4\sqrt{ }3}\)
tính:a,\(\dfrac{5.\left(38^2-17^2\right)}{8.\left(47^2-19^2\right)}\)
b, \(\sqrt{\dfrac{0,2.1,21.0,3}{7,5.3,2.0,64}}\)
c, \(\sqrt{3+\sqrt{5}}-\sqrt{3-\sqrt{5}}-\sqrt{2}\)
d, \(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}+\sqrt{7}\)
e, \(\sqrt{6,5+\sqrt{12}}+\sqrt{6,5-\sqrt{12}}+2\sqrt{6}\)
11) frac{3}{sqrt{6}-sqrt{3}}+frac{4}{sqrt{7}+sqrt{3}}
12) frac{6}{3sqrt{2}+2sqrt{3}}
13) left(sqrt{75}-3sqrt{2}-sqrt{12}right)left(sqrt{3}+sqrt{2}right)
14)frac{sqrt{5}+sqrt{3}}{sqrt{5}-sqrt{3}}+frac{sqrt{5}-sqrt{3}}{sqrt{5}+sqrt{3}}
15)frac{sqrt{5}-sqrt{3}}{sqrt{5}+sqrt{3}}+frac{sqrt{5}+sqrt{3}}{sqrt{5}-sqrt{3}}-frac{sqrt{5}+1}{sqrt{5}-1}
16)frac{sqrt{2}}{2sqrt{3}+4sqrt{2}}
17) frac{1}{4-3sqrt{2}}-frac{1}{4+3sqrt{2}}
18)frac{6}{sqrt{2}-sqrt{3}+3}
19)frac{sqrt{3+2sqrt{2}}+sqrt{3-2sqrt{2}...
Đọc tiếp
11) \(\frac{3}{\sqrt{6}-\sqrt{3}}+\frac{4}{\sqrt{7}+\sqrt{3}}\)
12) \(\frac{6}{3\sqrt{2}+2\sqrt{3}}\)
13) \(\left(\sqrt{75}-3\sqrt{2}-\sqrt{12}\right)\left(\sqrt{3}+\sqrt{2}\right)\)
14)\(\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}\)
15)\(\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}-\frac{\sqrt{5}+1}{\sqrt{5}-1}\)
16)\(\frac{\sqrt{2}}{2\sqrt{3}+4\sqrt{2}}\)
17) \(\frac{1}{4-3\sqrt{2}}-\frac{1}{4+3\sqrt{2}}\)
18)\(\frac{6}{\sqrt{2}-\sqrt{3}+3}\)
19)\(\frac{\sqrt{3+2\sqrt{2}}+\sqrt{3-2\sqrt{2}}}{\sqrt{3+2\sqrt{2}}-\sqrt{3-2\sqrt{2}}}\)
20)\(\sqrt{24}+6\sqrt{\frac{2}{3}}+\frac{10}{\sqrt{6}-1}\)
21)\(2\sqrt{40\sqrt{12}}-2\sqrt{\sqrt{75}}-3\sqrt{5\sqrt{58}}\)
22)\(4\sqrt{20}-3\sqrt{125}+5\sqrt{45}-15\sqrt{\frac{1}{5}}\)
23)\(\left(3\sqrt{8}-2\sqrt{12}+\sqrt{20}\right):\left(3\sqrt{18}-2\sqrt{27}+\sqrt{45}\right)\)
24)\(\left(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6}-2}-\frac{12}{3-\sqrt{6}}\right)\left(\sqrt{6}+11\right)\)
25)\(\left(\sqrt{7}-\sqrt{5}\right)^2+2\sqrt{35}\)
26)\(\frac{\sqrt{6}+\sqrt{14}}{2\sqrt{3}+\sqrt{28}}+\frac{3\sqrt{45}+\sqrt{243}}{\sqrt{5}+\sqrt{3}}\)
27)\(\frac{1}{\sqrt{7-\sqrt{24}}+1}-\frac{1}{\sqrt{7+\sqrt{24}}-1}\)
28)\(\frac{1}{2+\sqrt{3}}+\frac{1}{\sqrt{3}}-\frac{2}{3+\sqrt{3}}\)
29)\(\frac{3+\sqrt{5}}{2\sqrt{2}+\sqrt{3+\sqrt{5}}}+\frac{3-\sqrt{5}}{2\sqrt{2}-\sqrt{3-\sqrt{5}}}\)
30)\(\left(15\sqrt{50}+5\sqrt{200}-3\sqrt{450}\right):\sqrt{10}\)
31)\(\left(\frac{2}{\sqrt{3}-1}+\frac{3}{\sqrt{3}-2}+\frac{15}{3-\sqrt{3}}\right).\frac{1}{\sqrt{3}+5}\)
32)\(\frac{5+\sqrt{5}}{5-\sqrt{5}}+\frac{5-\sqrt{5}}{5+\sqrt{5}}-\sqrt{10}\)
Tính giá trị biểu thức
a, A = (1 - 1/1+2) . (1 - 1/1+2+3) . (1- 1/1+2+3+4) . ... .(1- 1/1+2+...+100)
b, B = (2/3+ 3/4 +...+99/100).(1/2+2/3+...+98/99) - (1/2+2/3+...+99/100).(2/3+3/4+...+98/99)
c, C = \(\frac{3^3+1^3}{2^3-1^3}+\frac{5^3+2^3}{3^3-2^3}+\frac{7^3+3^3}{4^3-3^3}+...+\frac{41^3+20^3}{21^3-20^3}\)