\(\sqrt{4+2\sqrt{3}+\sqrt{13+4\sqrt{3}}}=\sqrt{4+2\sqrt{3}+\sqrt{\left(12+2\cdot2\sqrt{3}\cdot1+1\right)}}=\sqrt{4+2\sqrt{3}+\sqrt{\left(2\sqrt{3}+1\right)^2}}=\sqrt{5+4\sqrt{3}}\)
Thực hiện phép tính:
a)\(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)
b)\(\left(\sqrt{3}-\sqrt{2}\right)\sqrt{5+2\sqrt{6}}\)
c)\(\sqrt{5-\sqrt{13+4\sqrt{3}}}+\sqrt{3+\sqrt{13+4\sqrt{3}}}\)
d)\(\sqrt{1+\sqrt{3+\sqrt{13+4\sqrt{3}}}}+\sqrt{1-\sqrt{3-\sqrt{13-4\sqrt{3}}}}\)
Mọi người giải gấp giúp em với!!!!
1/Tính
A=\(\dfrac{\sqrt{15-10\sqrt{2}}+\sqrt{13+4\sqrt{10}}-\sqrt{11+2\sqrt{10}}}{2\sqrt{3+2\sqrt{2}}+\sqrt{9-4\sqrt{2}}+\sqrt{12+8\sqrt{2}}}\)
B=\(\dfrac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2}+\sqrt{3}}+\dfrac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2}-\sqrt{3}}\)
C=\(\dfrac{\sqrt{2-\sqrt{3}}+\sqrt{4-\sqrt{15}}+\sqrt{10}}{\sqrt{23-3\sqrt{5}}}\)
D=\(\dfrac{\sqrt{4+\sqrt{3}}+\sqrt{4-\sqrt{3}}}{\sqrt{4+\sqrt{13}}}\)
2/So sánh
\(\sqrt{2017^2-1}-\sqrt{2016^2-1}\) và \(\dfrac{2.1016}{\sqrt{2017^2-1}+\sqrt{2016^2-1}}\)
Bài 1:
1.\(\sqrt{2-\sqrt{3}}\)
2.\(\sqrt{3+\sqrt{5}}\)
3.\(\sqrt{21-6\sqrt{6}}\)
4.\(\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}\)
5.\(\left(2-\sqrt{3}\right)\sqrt{7+4\sqrt{3}}\)
6.\(\sqrt{13+4\sqrt{10}}+\sqrt{13-4\sqrt{10}}\)
Câu 1: \(\sqrt{2-\sqrt{3}}\)
Câu 2:\(\sqrt{15-\sqrt{13+\sqrt{48}}}\)
Câu 3:\(\sqrt{48-10\sqrt{7+4\sqrt{3}}}\)
Câu 4:\(\sqrt{5-\sqrt{13+4\sqrt{3}}}\)
a) \(\sqrt{13-4\sqrt{3}}+\sqrt{7-4\sqrt{3}}\)
b) \(\sqrt{6+2\sqrt{5}}+\sqrt{6-2\sqrt{5}}\)
c) \(\sqrt{4+2\sqrt{3}}-\sqrt{4-2\sqrt{3}}\)
d) \(\sqrt{7+4\sqrt{3}}+\sqrt{7-4\sqrt{3}}\)
e) \(\sqrt{9+4\sqrt{5}}\)
f) \(\sqrt{23+8\sqrt{7}}\)
Gỉai giúp mk vs
\(\sqrt{21-6\sqrt{6}}\)
\(\sqrt{14-6\sqrt{5}}+\sqrt{14+6\sqrt{5}}\)
\(\left(3-\sqrt{2}\right)\sqrt{7+4\sqrt{3}}\)
\(\sqrt{13+4\sqrt{10}}+\sqrt{13-4\sqrt{10}}\)
\(\sqrt{6}\left(\sqrt{26+15\sqrt{3}}+\sqrt{26-15\sqrt{3}}\right)\)
Rút gọn biểu thức.
a) \(\sqrt{\left(1-\sqrt{2}\right)^2}-\sqrt{3+2\sqrt{2}}+\sqrt{\left(-2\right)^6}\)
b) \(\sqrt{7+4\sqrt{3}}+\sqrt{13-4\sqrt{3}}\)
Tính
a/ \(2\sqrt{\dfrac{9-\sqrt{77}}{2}}-\sqrt{\dfrac{2}{10-3\sqrt{11}}}\)
b/ \(\left(\sqrt{13}-1\right)\sqrt{\dfrac{2}{7-\sqrt{13}}}+\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
Rút gọn:
a.\(\sqrt{21-6\sqrt6}+\sqrt{9+2\sqrt{18}}-2\sqrt{6+3\sqrt{3}}\)
b.\(\sqrt{4+\sqrt{15}}-\sqrt{7-3\sqrt{5}}\)
c.\(\sqrt{\dfrac{13}{4}+\sqrt{3}}\)\(-\sqrt{\dfrac{7}{4}-\sqrt{3}}\)
