Rút gọn:
\(A=\sqrt{5-2\sqrt{3-\sqrt{3}}}-\sqrt{3+\sqrt{3}}+\sqrt{2+\sqrt{3}}\)
\(B=\frac{\sqrt{21+3\sqrt{5}}+\sqrt{21-3\sqrt{5}}}{\sqrt{21}+6\sqrt{11}}+\sqrt{11-6\sqrt{2}}\)
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 biểu thức
1)\(\sqrt{6+\sqrt{32}}\) - \(\sqrt{11-\sqrt{72}}\)
2) \(\sqrt{21-4\sqrt{5}}\) + \(\sqrt{21+4\sqrt{5}}\)
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 E=\(\left(\sqrt{3+\sqrt{5}}+\sqrt{7+3\sqrt{5}}\right)\cdot\left(\sqrt{21+6\sqrt{6}}+\sqrt{21-6\sqrt{6}}\right)\)
Rút gọn
C = 21(\(\sqrt{2+\sqrt{3}}\) -\(\sqrt{6-2\sqrt{5}}\))2-6(\(\sqrt{2-\sqrt{3}}\) +\(\sqrt{\left(3+\sqrt{5}\right)^2}\))
1. Chứng mình rằng:
a) \(\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{3}+\sqrt{4}}+\frac{1}{\sqrt{5}+\sqrt{6}}+...+\frac{1}{\sqrt{47}+\sqrt{48}}>3\)
b) \(\left(\sqrt{22}-3\sqrt{2}\right).\sqrt{10+3\sqrt{11}}=2\)
2. Rút gọn các biểu thức sau:
\(A=\frac{\sqrt{\sqrt{5}+2}}{\sqrt{2}}-\sqrt{\sqrt{5}-1}\)
\(B=\left(5+\sqrt{21}\right).\left(\sqrt{14}-\sqrt{6}\right).\sqrt{5+\sqrt{21}}\)
Rút gọn biểu thức:
B=\(21\left(\sqrt{2+\sqrt{3}}+\sqrt{3-\sqrt{5}}\right)^2-6\left(\sqrt{2-\sqrt{3}}+\sqrt{3+\sqrt{5}}\right)^2-15\sqrt{5}\)
Bài 1. thực hiện phép tính
a) \(\sqrt{\frac{5+\sqrt{21}}{5-\sqrt{21}}}+\sqrt{\frac{5-\sqrt{21}}{5+\sqrt{21}}}\) b) \(\sqrt{\frac{4+\sqrt{7}}{4-\sqrt{7}}}+\sqrt{\frac{4-\sqrt{7}}{4+\sqrt{7}}}\)
Bài 2. Tính:a) \(M=\left(2\sqrt{2}\right)\sqrt{2+4\sqrt{3+\sqrt{2}+\sqrt{11-6\sqrt{2}}}}\)
b) \(\frac{1}{\sqrt{25}+\sqrt{24}}+\frac{1}{\sqrt{24}+\sqrt{23}}+...+\frac{1}{\sqrt{2}+\sqrt{1}}=4\)
c)
\(\frac{\left(5\sqrt{3}+\sqrt{50}\right)\left(5-\sqrt{24}\right)}{\sqrt{75}0-5\sqrt{2}}\)