Đây phải là dấu cộng
B=\(\sqrt{3+\sqrt{5}}.\left(3+\sqrt{5}\right).\sqrt{2}.\left(\sqrt{5}-1\right)\)
B=\(\sqrt{6+2\sqrt{5}}.\left(3+\sqrt{5}\right).\left(\sqrt{5}-1\right)\)
B=\(\sqrt{\left(\sqrt{5}+1\right)^2}.\left(3+\sqrt{5}\right).\left(\sqrt{5}-1\right)\)
B=\(\left(\sqrt{5}+1\right).\left(\sqrt{5}-1\right).\left(3+\sqrt{5}\right)\)
B=12+4\(\sqrt{5}\)
Tính
a) \(\left(2-\sqrt{3}\right)\cdot\left(2+\sqrt{3}\right)\)
b) \(\left(2\sqrt{3}-\sqrt{5}\right)\cdot\left(2\sqrt{3}+\sqrt{5}\right)\)
TÍNH :
\(A=\sqrt{3+\sqrt{5+2\sqrt{3}}}\cdot\sqrt{3-\sqrt{5+2\sqrt{3}}}\)
\(B=\sqrt{4+\sqrt{8}}\cdot\sqrt{2+\sqrt{2+\sqrt{2}}}\cdot\sqrt{2-\sqrt{2+\sqrt{2}}}\)
\(C=\sqrt{2+\sqrt{3}}\cdot\sqrt{2+\sqrt{2+\sqrt{3}}}\cdot\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}\cdot\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}\)
\(D=\left[4+\sqrt{15}\right]\left[\sqrt{10}-\sqrt{6}\right]\cdot\sqrt{4-\sqrt{15}}\)
\(E=\left[3-\sqrt{5}\right]\cdot\sqrt{3+\sqrt{5}}\text{ }+\left[3+\sqrt{5}\right]\cdot\sqrt{3-\sqrt{5}}\)
\(\sqrt{3-\sqrt{5}}\cdot\left(\sqrt{10}-\sqrt{2}\right)\cdot\left(3+\sqrt{5}\right)\)
\(\left(\sqrt{2}+1\right)\cdot\left(\sqrt{3}+1\right)\cdot\left(\sqrt{6}+1\right)\cdot\left(5-2\sqrt{2}-\sqrt{3}\right)\)
Giúp mình giải bài trên với ạ. Cần gấp. Đầu bài yêu cầu: Tính
\(\left(3-\sqrt{5}\right)\cdot\sqrt{3+\sqrt{5}}+\left(3+\sqrt{5}\right)\cdot\sqrt{3-\sqrt{5}}\)
a) \(\left(2+\sqrt{3}\right)\cdot\sqrt{7-4\sqrt{3}}\)
b) \(\sqrt{4+2\sqrt{3}}-\sqrt{5+2\sqrt{6}}+\sqrt{2}+\sqrt{9-4\sqrt{5}}-\sqrt{9+4\sqrt{5}}\)
c) \(\sqrt{3-\sqrt{5}}\cdot\left(\sqrt{10}-\sqrt{2}\right)\left(3+\sqrt{5}\right)\)
Thực hiện các phép tính sau:
a, \(\left(\sqrt{6}+\sqrt{2}\right)\cdot\left(\sqrt{3}-2\right)\cdot\sqrt{\sqrt{3}+2}\)
b, \(\left(4+\sqrt{15}\right)\cdot\left(\sqrt{10}-\sqrt{6}\right)\cdot\sqrt{4-\sqrt{15}}\)
c, \(\sqrt{13-\sqrt{160}}-\sqrt{53+4\sqrt{90}}\)
d, \(\sqrt{6-2\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-\sqrt{128}}}}\)
Tính:
a) \(\sqrt{8x^3}\cdot\sqrt{2x}\left(x>0\right)\)
b) \(\sqrt{12x^5}\cdot\sqrt{3x}\left(x>0\right)\)
Chứng minh: \(\frac{1}{2\cdot\sqrt{1}}+\frac{1}{3\cdot\sqrt{2}}+\frac{1}{4\cdot\sqrt{3}}+...+\frac{1}{2012\cdot\sqrt{2011}}+\frac{1}{2013\cdot\sqrt{2012}}\)\(< 2\)
Chứng minh: A=\(\frac{1}{3\cdot\left(\sqrt{1}+\sqrt{2}\right)}+\frac{1}{5\cdot\left(\sqrt{2}+\sqrt{3}\right)}+...+\frac{1}{97\cdot\left(\sqrt{48}+\sqrt{49}\right)}\)\(< \frac{1}{2}\)