\(\text{Đặt }A=\sqrt{10+6\sqrt{2}}-\sqrt{10-6\sqrt{2}}\)
\(\Rightarrow A^2=10+6\sqrt{2}+10-6\sqrt{2}-2\sqrt{\left(10+6\sqrt{2}\right)\left(10-6\sqrt{2}\right)}\)
\(=20-2\sqrt{28}\Rightarrow A=\sqrt{20-2\sqrt{28}}\text{ hoặc }A=-\sqrt{20-2\sqrt{28}}\)
\(\text{Mà }A>0\left(\sqrt{20+6\sqrt{2}}>\sqrt{20-6\sqrt{2}}\right)\)
\(\text{Nên }A=\sqrt{20-2\sqrt{28}}\)
Bài 1 : rút gọn
1, \(\sqrt{6+2\sqrt{5}}\) 2, \(\sqrt{15-6\sqrt{6}}-\sqrt{10-4\sqrt{6}}\)
3. \(\sqrt{31-10\sqrt{6}}-\sqrt{\left(3-2\sqrt{6}\right)^2}\)
a)\(\sqrt{\left(2\sqrt{2}-3\right)^2+\sqrt{15}}\)
b)\(\sqrt{\left(\sqrt{10}-3\right)}^2+\sqrt{\left(\sqrt{10}-4\right)^2}\)
c)\(11+6\sqrt{2}=\left(3+\sqrt{2}\right)^2\)
d)\(\sqrt{11}+6\sqrt{2}+\sqrt{11-6\sqrt{2}=6}\)
Tính:
1) \(\sqrt{4-2\sqrt{3}}\)
2) \(\sqrt{5+2\sqrt{6}}\)
3) \(\sqrt{7-2\sqrt{10}}\)
4) \(\sqrt{14-6\sqrt{6}}\)
5) \(\sqrt{8+2\sqrt{15}}\)
6) \(\sqrt{10-2\sqrt{21}}\)
7) \(\sqrt{11+2\sqrt{18}}\)
LÀM CHI TIẾT GIÚP MK NHÉ!
a)\(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
b)\(\frac{6+4\sqrt{2}}{\sqrt{2}+\sqrt{6+4\sqrt{2}}}+\frac{6-4\sqrt{2}}{\sqrt{2}-\sqrt{6-4\sqrt{2}}}\)
Rút gọn:
\(A=\sqrt{11-2\sqrt{10}}+\sqrt{9-2\sqrt{4}}-\sqrt{10}-\sqrt{7}\)
\(B=\frac{\sqrt{3}+\sqrt{11+2\sqrt{6}}-\sqrt{5+2\sqrt{6}}}{\sqrt{2}+\sqrt{6+2\sqrt{5}}-\sqrt{7+2\sqrt{10}}}\)
Rút gọn căn thức :
A = \(\frac{\sqrt{10}+2\sqrt{6}+\sqrt{10}.\sqrt{4+\sqrt{15}}}{\sqrt{2}+\sqrt{3}+\sqrt{5}}\)\(\frac{\sqrt{10}+2\sqrt{6}+\sqrt{10}.\sqrt{4+\sqrt{15}}}{\sqrt{2}+\sqrt{3}+\sqrt{5}}\)
nhờ anh chị giải giúp em !
10)\(\sqrt{10+2\sqrt{6}+2\sqrt{10}+2\sqrt{15}}\)
11)\(\sqrt{10-2\sqrt{6}+2\sqrt{10}-2\sqrt{15}}\)
\(\frac{\sqrt{10+6\sqrt{2}}-\sqrt{10-6\sqrt{2}}-\sqrt{9+2\sqrt{20}}}{\sqrt{5-\sqrt{7}}}\)
\(\frac{2\sqrt{15}-2\sqrt{10}+\sqrt{6}-3}{2\sqrt{5}-2\sqrt{10}-\sqrt{3}+\sqrt{6}}\)
Tính
\(D=\sqrt{6+2\sqrt{8\sqrt{2}-9}}-\sqrt{7-\sqrt{2}}.\)
\(B=\sqrt{29+6\sqrt{6}}-\sqrt{32-6\sqrt{15}}\)
\(A=\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
