\(=\dfrac{\sqrt{5}+1+\sqrt{5}-1}{\sqrt{2}}=\sqrt{10}\)
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Chương I - Căn bậc hai. Căn bậc ba
Các câu hỏi tương tự
Tính giá trị các biểu thức sau:
a) Asqrt{frac{2+sqrt{3}}{2-sqrt{3}}}+sqrt{frac{2-sqrt{3}}{2+sqrt{3}}}
b) Afrac{sqrt{3-2sqrt{2}}}{sqrt{17-12sqrt{2}}}-frac{sqrt{3+2sqrt{2}}}{sqrt{17+12sqrt{2}}}
c) Afrac{sqrt{5}+sqrt{3}}{sqrt{5}-sqrt{3}}+frac{sqrt{5}-sqrt{3}}{sqrt{5}+sqrt{3}}
c) Afrac{sqrt{5}-sqrt{3}}{sqrt{5}+sqrt{3}}+frac{sqrt{5}+sqrt{3}}{sqrt{5}-sqrt{3}}-frac{sqrt{5}+1}{sqrt{5}-1}
Đọc tiếp
Tính giá trị các biểu thức sau:
a) \(A=\sqrt{\frac{2+\sqrt{3}}{2-\sqrt{3}}}+\sqrt{\frac{2-\sqrt{3}}{2+\sqrt{3}}}\)
b) \(A=\frac{\sqrt{3-2\sqrt{2}}}{\sqrt{17-12\sqrt{2}}}-\frac{\sqrt{3+2\sqrt{2}}}{\sqrt{17+12\sqrt{2}}}\)
c) \(A=\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}\)
c) \(A=\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}-\frac{\sqrt{5}+1}{\sqrt{5}-1}\)
Tính
\(a.\dfrac{9\sqrt{5}+3\sqrt{27}}{\sqrt{5}+\sqrt{3}}\)
\(b.\left(3-\sqrt{5}\right).\sqrt{3+\sqrt{5}}+\left(3+\sqrt{5}\right).\sqrt{3-\sqrt{5}}\)
\(c.\dfrac{a-\sqrt{b}}{\sqrt{b}}:\dfrac{\sqrt{b}}{a+\sqrt{b}}\left(b>0;a\ne-\sqrt{b}\right)\)
Tính
1) sqrt{9-4sqrt{5}}
2) 2sqrt{3}+sqrt{48}-sqrt{75}-sqrt{243}
3) sqrt{4+sqrt{8}}.sqrt{2+sqrt{2+sqrt{2}}}.sqrt{2-sqrt{2+sqrt{2}}}
4) sqrt{3+2sqrt{2}}-sqrt{6-4sqrt{2}}
5) dfrac{sqrt{5}-sqrt{3}}{sqrt{5}+sqrt{3}}+dfrac{sqrt{5}+sqrt{3}}{sqrt{5}-sqrt{3}}-dfrac{sqrt{5}+1}{sqrt{5}-1}
6) sqrt{5sqrt{3}+5sqrt{48-10sqrt{7+4sqrt{3}}}}
Đọc tiếp
Tính
1) \(\sqrt{9-4\sqrt{5}}\)
2) \(2\sqrt{3}+\sqrt{48}-\sqrt{75}-\sqrt{243}\)
3) \(\sqrt{4+\sqrt{8}}.\sqrt{2+\sqrt{2+\sqrt{2}}}.\sqrt{2-\sqrt{2+\sqrt{2}}}\)
4) \(\sqrt{3+2\sqrt{2}}-\sqrt{6-4\sqrt{2}}\)
5) \(\dfrac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\dfrac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}-\dfrac{\sqrt{5}+1}{\sqrt{5}-1}\)
6) \(\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)
rút gọn A)\(\sqrt{\sqrt{5}-\sqrt{3-\left(2\sqrt{5-3}\right)^2}}\)
B) \(\sqrt{6+2\sqrt{5-\sqrt{\left(2\sqrt{3+1}\right)^2}}}\)
C) \(\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{\left(2+\sqrt{3}\right)^2}}}}\)
4 tháng 7 2021 lúc 16:12
* Rút gọn biểu thức
a. \(3\sqrt{2}-4\sqrt{18}+2\sqrt{32}-\sqrt{50}\)
b. \(\sqrt{\left(\sqrt{2}-\sqrt{3}\right)^2}+\sqrt{18}\)
c. \(5\sqrt{\dfrac{1}{5}}+\dfrac{1}{3}\sqrt{45}+\dfrac{5-\sqrt{5}}{\sqrt{5}}\)
d. \(\sqrt{7-4\sqrt{3}}+\sqrt{\left(1+\sqrt{3}\right)^2}\)
Tính:
\(A=\left(\sqrt{72}-3\sqrt{24}+5\sqrt{8}\right)\sqrt{2}+4\sqrt{27}\)
\(B=\dfrac{1}{\sqrt{2}-1}+\dfrac{14}{3+\sqrt{2}}\)
\(C=\dfrac{5+3\sqrt{5}}{\sqrt{5}}+\dfrac{3\sqrt{3}}{\sqrt{3}+1}-\left(\sqrt{5}+3\right)\)
\(D=\sqrt{\left(1-\sqrt{2}\right)^2}-3\sqrt{18}+4\sqrt{\dfrac{1}{2}}\)
Tính ;
a) sqrt{4+sqrt{8}}.sqrt{2+sqrt{2+sqrt{2}}.}sqrt{2-sqrt{2+sqrt{2}}}
b) sqrt{47+sqrt{5}}.sqrt{7-sqrt{2+sqrt{5}}}.sqrt{7+sqrt{2+sqrt{5}}}
c) sqrt{2+sqrt{3}}.sqrt{2+sqrt{2+sqrt{3}}}.sqrt{2+sqrt{2+sqrt{2+sqrt{3}}}}.sqrt{2-sqrt{2+sqrt{2+sqrt{3}}}}
d) sqrt{31+sqrt{2}}.sqrt{6+sqrt{5+sqrt{2}}}sqrt{3+sqrt{3+sqrt{5+sqrt{2}}}}.sqrt{3-sqrt{3+sqrt{5+sqrt{2}}}}
Đọc tiếp
Tính ;
a) \(\sqrt{4+\sqrt{8}}.\sqrt{2+\sqrt{2+\sqrt{2}}.}\sqrt{2-\sqrt{2+\sqrt{2}}}\)
b) \(\sqrt{47+\sqrt{5}}.\sqrt{7-\sqrt{2+\sqrt{5}}}.\sqrt{7+\sqrt{2+\sqrt{5}}}\)
c) \(\sqrt{2+\sqrt{3}}.\sqrt{2+\sqrt{2+\sqrt{3}}}.\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}.\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}\)
d) \(\sqrt{31+\sqrt{2}}.\sqrt{6+\sqrt{5+\sqrt{2}}}\sqrt{3+\sqrt{3+\sqrt{5+\sqrt{2}}}}.\sqrt{3-\sqrt{3+\sqrt{5+\sqrt{2}}}}\)
U = \(\left(\frac{1}{2-\sqrt{5}}+\frac{2}{\sqrt{5}+\sqrt{3}}\right):\frac{1}{\sqrt{21-12\sqrt{3}}}\)
*W = \(\frac{5\sqrt{3}}{\sqrt{3-\sqrt{5}-\sqrt{3}}}-\frac{5\sqrt{3}}{\sqrt{3-\sqrt{5}+\sqrt{3}}}\)
Y = \(\frac{\sqrt{2}}{2\sqrt{2}+\sqrt{3+\sqrt{5}}}\)
Rút gọn biểu thức sau
\(a.\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{4}}{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}\)
\(b.\dfrac{\sqrt{\dfrac{5}{3}}+\sqrt{\dfrac{3}{5}}-2}{\sqrt{\dfrac{5}{3}}-\sqrt{\dfrac{3}{5}}}\)
Câu 1 :Tính : B ( 3 - sqrt{5}) ( sqrt{5} + 3 )Câu 2 : Rút gọn : dfrac{sqrt{5}+1}{3-2sqrt{2}}-dfrac{sqrt{10}}{sqrt{5}-2}+3left(sqrt{2}-sqrt{5}right)Câu 3: left(dfrac{sqrt{x}+sqrt{y}}{1-sqrt{xy}}+dfrac{sqrt{x}+sqrt{y}}{1+sqrt{xy}}right):left(1+dfrac{x+y+2xy}{1-xy}right)a, Rút gọn biểu thức ab, Tính giá trị của A khi x + dfrac{2}{2+sqrt{3}}
Đọc tiếp
Câu 1 :Tính : B = ( 3 - \(\sqrt{5}\)) ( \(\sqrt{5}\) + 3 )
Câu 2 : Rút gọn : \(\dfrac{\sqrt{5}+1}{3-2\sqrt{2}}-\dfrac{\sqrt{10}}{\sqrt{5}-2}+3\left(\sqrt{2}-\sqrt{5}\right)\)
Câu 3: \(\left(\dfrac{\sqrt{x}+\sqrt{y}}{1-\sqrt{xy}}+\dfrac{\sqrt{x}+\sqrt{y}}{1+\sqrt{xy}}\right):\left(1+\dfrac{x+y+2xy}{1-xy}\right)\)
a, Rút gọn biểu thức a
b, Tính giá trị của A khi x + \(\dfrac{2}{2+\sqrt{3}}\)