\(A^2=4+\sqrt{10+2\sqrt{5}}+2.\sqrt{\left(4+\sqrt{10+2\sqrt{5}}\right).\left(4-\sqrt{10+2\sqrt{5}}\right)}+4-\sqrt{10+2\sqrt{5}}\)
\(A^2=8+2.\sqrt{4^2-\left(10+2\sqrt{5}\right)}=8+2.\sqrt{6-2\sqrt{5}}\)
\(A^2=8+2.\sqrt{5-2\sqrt{5}.1+1}=8+2.\sqrt{\left(\sqrt{5}-1\right)^2}=8+2.\left(\sqrt{5}-1\right)\)
\(A^2=6+2\sqrt{5}=5+2\sqrt{5}+1=\left(\sqrt{5}+1\right)^2\)
=> \(A=\sqrt{5}+1\) (Do A > 0)
\(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\) rút gọn
5.Rút gọn:
B= \(\sqrt{6-2\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-8\sqrt{2}}}}\)
6.Rút gọn:
A= \(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
RÚT GỌN A=\(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4+\sqrt{10+2\sqrt{5}}}\)
Rút gọn:
A = \(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
B = \(\sqrt{4+\sqrt{15}}+\sqrt{4-\sqrt{15}}-2\sqrt{3-\sqrt{5}}\)
Rút gọn:
\(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}
\)
Rút gọn căn thức :
A = \(\frac{\sqrt{10}+2\sqrt{6}+\sqrt{10}.\sqrt{4+\sqrt{15}}}{\sqrt{2}+\sqrt{3}+\sqrt{5}}\)\(\frac{\sqrt{10}+2\sqrt{6}+\sqrt{10}.\sqrt{4+\sqrt{15}}}{\sqrt{2}+\sqrt{3}+\sqrt{5}}\)
Rút gọn biểu thức: \(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
rút gọn biểu thức
A=\(\sqrt{4+\sqrt{10+2\sqrt{5}}}\)+\(\sqrt{4-\sqrt{10-2\sqrt{5}}}\)
rút gọn biểu thức :
A= \(\dfrac{\sqrt{4+\sqrt{3}}+\sqrt{4-\sqrt{3}}}{\sqrt{4+\sqrt{13}}}+\sqrt{27-10\sqrt{2}}\).
B= \(\dfrac{\sqrt{2-\sqrt{3}}+\sqrt{4-\sqrt{15}}+\sqrt{10}}{\sqrt{23-3\sqrt{5}}}\).
C= \(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\).
