\(\sqrt{21-8\sqrt{5}}\)\(-\sqrt{21-4\sqrt{5}}\)
\(=\sqrt{16-2.4\sqrt{5}+5}\)\(-\sqrt{20-2\sqrt{20}+1}\)
\(=\sqrt{\left(4-\sqrt{5}\right)^2}\)\(-\sqrt{\left(\sqrt{20}-1\right)}\)
\(=4-\sqrt{5}-\left(\sqrt{20}-1\right)\)
\(=4-\sqrt{5}-\sqrt{20}+1\)
\(=5-\sqrt{5}-2\sqrt{5}\)
\(=5-3\sqrt{5}\)
Rút gọn biểu thức
1)\(\sqrt{6+\sqrt{32}}\) - \(\sqrt{11-\sqrt{72}}\)
2) \(\sqrt{21-4\sqrt{5}}\) + \(\sqrt{21+4\sqrt{5}}\)
Thực hiện phép tính (rút gọn biểu thức)
a)\(\left(\sqrt{3}-2\right)\sqrt{7+4\sqrt{3}}\)
b) \(\sqrt{6+\sqrt{32}}\) - \(\sqrt{11-\sqrt{72}}\)
c) \(\sqrt{21-4\sqrt{5}}\) + \(\sqrt{21+4\sqrt{5}}\)
Rút gọn \(\sqrt{6+2.\sqrt{5}}+\sqrt{21-8.\sqrt{5}}\)
Rút Gọn :
\(A=\sqrt{\frac{5+\sqrt{21}}{5-\sqrt{21}}}+\sqrt{\frac{5-\sqrt{21}}{5+\sqrt{21}}}\)
\(B=\sqrt{7+\sqrt{33}}+\sqrt{7-\sqrt{33}}\)
\(A=\sqrt{5+\sqrt{21}}+\sqrt{5-\sqrt{21}}-2\sqrt{4-\sqrt{7}}\)
rút gọn
Rút gọn M=\(\frac{\sqrt{21+3\sqrt{5}}+\sqrt{21-3\sqrt{5}}}{\sqrt{21}+6\sqrt{11}}+\sqrt{11-6\sqrt{2}}\)
Rút Gọn
\(A=\sqrt{5+\sqrt{21}}+\sqrt{5-\sqrt{21}}\)
rút gọn E=\(\left(\sqrt{3+\sqrt{5}}+\sqrt{7+3\sqrt{5}}\right)\cdot\left(\sqrt{21+6\sqrt{6}}+\sqrt{21-6\sqrt{6}}\right)\)
\(\frac{8+2\sqrt{15}+\sqrt{21}+\sqrt{35}}{\sqrt{3}+\sqrt{5}+\sqrt{7}}\)
rút gọn
