đặt A= \(\sqrt{2-\sqrt{3}}-\sqrt{2+\sqrt{3}}\)
\(\Leftrightarrow A^2=4-2\sqrt{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}\)
=4-2=2
\(\Leftrightarrow A=\sqrt{2}\)
Hay \(\sqrt{2-\sqrt{3}}-\sqrt{2+\sqrt{3}}\)=\(\sqrt{2}\)
Chương I - Căn bậc hai. Căn bậc ba
Các câu hỏi tương tự
\(\sqrt{2+\sqrt{3}}.\sqrt{2+\sqrt{2+\sqrt{3}}}.\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}.\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}\)
\(\sqrt{2+\sqrt{2}}.\sqrt{3+\sqrt{7+\sqrt{2}}}.\sqrt{3+\sqrt{6+\sqrt{7+\sqrt{2}}}}.\sqrt{3-\sqrt{6+\sqrt{7+\sqrt{2}}}}\)
Rút gọn\(\dfrac{\sqrt{2+\sqrt{3}+\sqrt{2-\sqrt{3}}}}{\sqrt{2+\sqrt{3}-\sqrt{2-\sqrt{3}}}}+\dfrac{\sqrt{2+\sqrt{3}-\sqrt{2-\sqrt{3}}}}{\sqrt{2+\sqrt{3}+\sqrt{2-\sqrt{3}}}}\)
Tính:
\(\sqrt{2+\sqrt{3}}.\sqrt{2+\sqrt{2+\sqrt{3}}}.\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}.\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}\)
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) \(\sqrt{31+\sqrt{2}}.\sqrt{6+\sqrt{5+\sqrt{2}}}\sqrt{3+\sqrt{3+\sqrt{5+\sqrt{2}}}}.\sqrt{3-\sqrt{3+\sqrt{5+\sqrt{2}}}}\)
Rút gọn : \(\dfrac{\sqrt{45+27\sqrt{2}}+\sqrt{45-27\sqrt{2}}}{\sqrt{5+3\sqrt{2}}-\sqrt{5-3\sqrt{2}}}-\dfrac{\sqrt{3+\sqrt{2}}+\sqrt{3-\sqrt{2}}}{\sqrt{3+\sqrt{2}}-\sqrt{3-\sqrt{2}}}\)
22 tháng 7 2021 lúc 9:14
Tính:
a)\(\sqrt{3\sqrt{2}-2\sqrt{3}}\cdot\sqrt{3\sqrt{2}+2\sqrt{3}}\)
b) \(\sqrt{2+2\sqrt{2-\sqrt{2}}}\cdot\sqrt{2-2\sqrt{2-\sqrt{2}}}\)
c)\(\left(\sqrt{2}-\sqrt{7}\right)\sqrt{9+2\sqrt{14}}\)
Rút gọn:
\(A=\dfrac{\sqrt{3}-3}{\sqrt{2-\sqrt{3}}+2\sqrt{2}}+\dfrac{\sqrt{3}+3}{\sqrt{2+\sqrt{3}}-2\sqrt{2}}\)
\(B=\dfrac{\sqrt{11+2\sqrt{30}}-\sqrt{11-2\sqrt{30}}}{\sqrt{5}}\)
\(C=2\sqrt{3+\sqrt{5}}-\left(\sqrt{4+\sqrt{15}}+\sqrt{4-\sqrt{15}}\right)\)
\(D=\sqrt{\dfrac{2+\sqrt{3}}{2-\sqrt{3}}}+\sqrt{\dfrac{2-\sqrt{3}}{2+\sqrt{3}}}\)
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) \(A=\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}-\frac{\sqrt{5}+1}{\sqrt{5}-1}\)
D sqrt{94-42sqrt{5}}-sqrt{94+42sqrt{5}}
A sqrt{sqrt{5}-sqrt{3-sqrt{29-12sqrt{5}}}}
C dfrac{2sqrt{4-sqrt{5+sqrt{21+sqrt{80}}}}}{sqrt{10}-sqrt{2}}
F sqrt{2+sqrt{3}}cdotsqrt{2+sqrt{2+sqrt{3}}cdotsqrt{2+sqrt{2+sqrt{2+sqrt{3}}}}}cdotsqrt{2-sqrt{2+sqrt{2+sqrt{3}}}}
B dfrac{1}{sqrt{1}+sqrt{2}}+dfrac{1}{sqrt{2}+sqrt{3}}+dfrac{1}{sqrt{3}+sqrt{4}}+...+dfrac{1}{sqrt{n-1}+sqrt{n}}
E dfrac{1}{sqrt{1}-sqrt{2}}-dfrac{1}{sqrt{2}-sqrt{3}}+dfrac{1}{sqrt{3}-sqrt{4}}-...-dfrac{1}{sqrt{24}-sqrt{25}}
Đọc tiếp
D = \(\sqrt{94-42\sqrt{5}}-\sqrt{94+42\sqrt{5}}\)
A = \(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
C = \(\dfrac{2\sqrt{4-\sqrt{5+\sqrt{21+\sqrt{80}}}}}{\sqrt{10}-\sqrt{2}}\)
F = \(\sqrt{2+\sqrt{3}}\cdot\sqrt{2+\sqrt{2+\sqrt{3}}\cdot\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}}\cdot\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}\)
B = \(\dfrac{1}{\sqrt{1}+\sqrt{2}}+\dfrac{1}{\sqrt{2}+\sqrt{3}}+\dfrac{1}{\sqrt{3}+\sqrt{4}}+...+\dfrac{1}{\sqrt{n-1}+\sqrt{n}}\)
E = \(\dfrac{1}{\sqrt{1}-\sqrt{2}}-\dfrac{1}{\sqrt{2}-\sqrt{3}}+\dfrac{1}{\sqrt{3}-\sqrt{4}}-...-\dfrac{1}{\sqrt{24}-\sqrt{25}}\)
Rút gọn các biểu thức sau:
a) dfrac{2}{5}sqrt{75}-0,5sqrt{48}+sqrt{300}-dfrac{2}{3}sqrt{12}
b) dfrac{9-2sqrt{3}}{3sqrt{6}-2sqrt{2}}+dfrac{3}{3+sqrt{6}}
c) 3sqrt{2}-2sqrt{3}+2sqrt{3}+3sqrt{2}
d) sqrt{15-6sqrt{6}}+sqrt{33-12sqrt{6}}
e) dfrac{sqrt{a}-sqrt{b}^2+4sqrt{ab}}{sqrt{a}+sqrt{b}}-dfrac{asqrt{b}-bsqrt{a}}{sqrt{ab}} với a 0, b 0
Đọc tiếp
Rút gọn các biểu thức sau:
a) \(\dfrac{2}{5}\sqrt{75}-0,5\sqrt{48}+\sqrt{300}-\dfrac{2}{3}\sqrt{12}\)
b) \(\dfrac{9-2\sqrt{3}}{3\sqrt{6}-2\sqrt{2}}+\dfrac{3}{3+\sqrt{6}}\)
c) \(3\sqrt{2}-2\sqrt{3}+2\sqrt{3}+3\sqrt{2}\)
d) \(\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}\)
e) \(\dfrac{\sqrt{a}-\sqrt{b}^2+4\sqrt{ab}}{\sqrt{a}+\sqrt{b}}-\dfrac{a\sqrt{b}-b\sqrt{a}}{\sqrt{ab}}\) với a > 0, b > 0