Đặt \(A=\sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}}\)
\(A^2=2+\sqrt{3}+2-\sqrt{3}+2\sqrt{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}\)
\(A^2=4+2\sqrt{4-3}=4+2=6\)
=> A = can 6
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 :\(R=\sqrt{2+\sqrt{3}}.\sqrt{2+\sqrt{2+\sqrt{3}}}.\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}.\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}\)
Tính :\(R=\sqrt{2+\sqrt{3}}.\sqrt{2+\sqrt{2+\sqrt{3}}}.\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}.\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}\)
Tính \(R=\sqrt{2+\sqrt{3}}.\sqrt{2+\sqrt{2+\sqrt{3}}}.\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}.\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}\)
Tính :
\(R= \sqrt{2+\sqrt{3}}. \sqrt{2+\sqrt{2 +\sqrt{3}}}. \sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}.\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}\)
TÍnh \(\sqrt{2+\sqrt{3}}+\sqrt{2+\sqrt{2+\sqrt{3}}}+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}+\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}\)
Tính Q=\(\frac{\sqrt{45+27\sqrt{2}}+\sqrt{45-27\sqrt{2}}}{\sqrt{5+3\sqrt{2}}-\sqrt{5-3\sqrt{2}}}-\frac{\sqrt{3+\sqrt{2}}+\sqrt{3-\sqrt{2}}}{\sqrt{3+\sqrt{2}}-\sqrt{3-\sqrt{2}}}\)
1. Tính A= \(\dfrac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
Thực hiện các phép tính :
1. \(A=\sqrt{2-\sqrt{3}}\sqrt{2+\sqrt{2-\sqrt{3}}}\sqrt{2+\sqrt{2+\sqrt{2-\sqrt{3}}}}\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2-\sqrt{3}}}}}\)
2. \(B=\left(\dfrac{1}{1+\sqrt{2}}+\dfrac{2}{2+\sqrt{3}}+...+\dfrac{1}{20+\sqrt{21}}\right)\cdot2022\)
Giải chi tiết giúp mình ạ
\(\sqrt{3\sqrt{2}-2\sqrt{3}}\) . \(\sqrt{3\sqrt{2}+2\sqrt{3}}\)
tính !!!
