\(\sqrt{5-\sqrt{21}}+\sqrt{5-\sqrt{21}}=2\sqrt{5-\sqrt{21}}\)
\(=\sqrt{4}\sqrt{5-\sqrt{21}}=\sqrt{4.\left(5-\sqrt{21}\right)}\)
\(=\sqrt{20-4\sqrt{21}}=\sqrt{20-2\sqrt{4}\sqrt{21}}\)
\(=\sqrt{20-2\sqrt{84}}=\sqrt{14-2.\sqrt{14}\sqrt{6}+6}\)
\(=\sqrt{\left(\sqrt{14}-\sqrt{6}\right)^2}=\sqrt{14}-\sqrt{6}\)
\(\sqrt{\frac{5+\sqrt{21}}{5-\sqrt{21}}}+\sqrt{\frac{5-\sqrt{21}}{5+\sqrt{21}}}\)
\(\sqrt{\frac{5+\sqrt{21}}{5-\sqrt{21}}}+\sqrt{\frac{5-\sqrt{21}}{5+\sqrt{21}}}\)
Rút Gọn :
\(A=\sqrt{\frac{5+\sqrt{21}}{5-\sqrt{21}}}+\sqrt{\frac{5-\sqrt{21}}{5+\sqrt{21}}}\)
\(B=\sqrt{7+\sqrt{33}}+\sqrt{7-\sqrt{33}}\)
Tính:
i) \(\sqrt{8-3\sqrt{7}}+\sqrt{4-\sqrt{7}}\)
j) \(\sqrt{5+\sqrt{21}}-\sqrt{5-\sqrt{21}}\)
k) \(\sqrt{9-3\sqrt{5}}-\sqrt{9+3\sqrt{5}}\)
Rút gọn M=\(\frac{\sqrt{21+3\sqrt{5}}+\sqrt{21-3\sqrt{5}}}{\sqrt{21}+6\sqrt{11}}+\sqrt{11-6\sqrt{2}}\)
tính
\(\sqrt{2}\) ✖ (\(\sqrt{21}+3\)) ✖ \(\sqrt{5-\sqrt{21}}\)
\(\sqrt{2}\times\left(\sqrt{5}-1\right)\times\sqrt{3+\sqrt{5}}\)
Rút gọn biểu thức
1)\(\sqrt{6+\sqrt{32}}\) - \(\sqrt{11-\sqrt{72}}\)
2) \(\sqrt{21-4\sqrt{5}}\) + \(\sqrt{21+4\sqrt{5}}\)
Rút gọn:
\(A=\sqrt{5-2\sqrt{3-\sqrt{3}}}-\sqrt{3+\sqrt{3}}+\sqrt{2+\sqrt{3}}\)
\(B=\frac{\sqrt{21+3\sqrt{5}}+\sqrt{21-3\sqrt{5}}}{\sqrt{21}+6\sqrt{11}}+\sqrt{11-6\sqrt{2}}\)
Tính:
A =\(\sqrt{5-2\sqrt{3-\sqrt{3}}}-\sqrt{3+\sqrt{3}}+\sqrt{2+\sqrt{3}}\)
B= \(\frac{\sqrt{21+3\sqrt{5}}+\sqrt{21-3\sqrt{5}}}{\sqrt{21}+6\sqrt{11}}+\sqrt{11-6\sqrt{2}}\)
Rút gọn
a) \(\sqrt{\sqrt{2}-1}+\sqrt{\sqrt{2}+1}-\sqrt{\sqrt{2}+2}\)
b) \(\left(5+\sqrt{21}\right)\left(\sqrt{14}-\sqrt{6}\right)\sqrt{5-\sqrt{21}}\)
