\(A=\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}\)
\(=\sqrt{\left(\sqrt{2}+\sqrt{3}\right)^2}-\sqrt{\left(\sqrt{2}-\sqrt{3}\right)^2}\)
\(=\sqrt{2}+\sqrt{3}-\left(\sqrt{3}-\sqrt{2}\right)\)
\(=\sqrt{2}+\sqrt{3}-\sqrt{3}+\sqrt{2}\)
\(=2\sqrt{2}\)
\(A=\sqrt{4x+20}-2\sqrt{x+5}+\sqrt{9x+45}\)
a) Rút gọn A
b) Tìm x để A=6
rút gọn các biểu thức sau:
a,\(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
b,\(\sqrt{6+2\sqrt{5}-\sqrt{29-12\sqrt{5}}}\)
c,\(\sqrt{2+\sqrt{5-\sqrt{13-\sqrt{48}}}}\)
d,\(\left(3-\sqrt{5}\right)\sqrt{3+\sqrt{5}}+\left(3+\sqrt{5}\right)\sqrt{3-\sqrt{5}}\)
Rút gọn:
\(A=\sqrt{3+2\sqrt{2}}-\sqrt{6+2\sqrt{2}+2\sqrt{3}+2\sqrt{6}}\)
rút gọn
\(\frac{\sqrt{3}\sqrt{11+6\sqrt{2}}-\sqrt{5+2\sqrt{6}}}{\sqrt{2}+\sqrt{6+2\sqrt{5}}-\sqrt{7+2\sqrt{10}}}\)
b, \(\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)
rút gọn biểu thức sau
a/\(\sqrt{6+2\sqrt{5}}\) - \(\sqrt{6-2\sqrt{5}}\)
b/ \(\sqrt{7+3\sqrt{6}}\)+ \(\sqrt{7-2\sqrt{6}}\)- \(2\sqrt{6}\)
c/ \(\sqrt{9+4\sqrt{5}}\) +\(\sqrt{9-4\sqrt{5}}\)- \(2\sqrt{5}\)
1. Rút gọn các biểu thức sau:
E = \(\sqrt{37-6\sqrt{30}}\)
F = \(\sqrt{51-6\sqrt{30}}\)
G = \(\sqrt{59-6\sqrt{30}}\)
H = \(\sqrt{17-2\sqrt{30}}\)
rút gọn M=\(\left(\sqrt{6}+\sqrt{2}\right)\left(\sqrt{3}-2\right)\sqrt{\sqrt{3}+2}\)
Rút gọn
a) \(A=\left(\frac{\sqrt{10}-\sqrt{5}}{\sqrt{8}-2}-\frac{\sqrt{90}}{3}\right).\frac{1}{\sqrt{5}}\)
b) \(B=\left(\frac{\sqrt{26}-\sqrt{13}}{1-\sqrt{2}}+\frac{\sqrt{18}-\sqrt{6}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{13}-\sqrt{6}}\)
c) \(C=\frac{\sqrt{10+2\sqrt{21}}-\sqrt{5-2\sqrt{6}}}{\sqrt{9-2\sqrt{14}}}\)
Rút gọn: a) \(\sqrt{4+2\sqrt{3}}-\sqrt{5+2\sqrt{6}}+\sqrt{2}\)
b) \(\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)
