\(=\sqrt{13+30\sqrt{2+\sqrt{\left(2\sqrt{2}+1\right)^2}}}\)
\(=\sqrt{13+30\sqrt{2+2\sqrt{2}+1}}=\sqrt{13+30\sqrt{3+2\sqrt{2}}}\)
\(=\sqrt{13+30\sqrt{\left(\sqrt{2}+1\right)^2}}\)
\(=\sqrt{13+30+30\sqrt{2}}=\sqrt{43+30\sqrt{2}}\)
\(=\sqrt{\left(5+3\sqrt{2}\right)^2}=5+3\sqrt{2}\)
Rút gọn
a, \(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)
b,\(\sqrt{227-30\sqrt{2}}+\sqrt{123+22\sqrt{2}}\)
Tính:
\(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}-3\sqrt{2}}}}\)
Rút gọn \(A=\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)
\(B=\sqrt{4+\sqrt{5\sqrt{3+5\sqrt{48-10\sqrt{7}+4\sqrt{3}}}}}\)
Tính
\(\sqrt{13+30\sqrt{2+9+4\sqrt{2}}}\)
Tính:
a) \(A=3\sqrt{2}\left(\sqrt{50}-2\sqrt{18}+\sqrt{98}\right)\)
b) \(B=\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)
Rút gọn biểu thức:
a) \(\dfrac{\sqrt{9-2\sqrt{6}}-\sqrt{6}}{\sqrt{3}}\) b)\(\dfrac{5+\sqrt{5}}{5-\sqrt{5}}+\dfrac{5-\sqrt{5}}{5+\sqrt{5}}\)
c) \(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\) d) \(\sqrt{8+2\sqrt{10+2\sqrt{5}}}+\sqrt{8-2\sqrt{10+2\sqrt{5}}}\)
e) \(\dfrac{2\sqrt{3+\sqrt{5-\sqrt{13+\sqrt{48}}}}}{\sqrt{6}-\sqrt{2}}\) f) \(\sqrt{9-\sqrt{5\sqrt{3}+5\sqrt{8+10\sqrt{7-4\sqrt{3}}}}}\)
\(\sqrt{3+\sqrt{5}}+\sqrt{3-\sqrt{5}}\)
\(\sqrt{8-2\sqrt{15}}-\sqrt{23-4\sqrt{5}}\)
\(\sqrt{13+30\sqrt{2+\sqrt{9+\sqrt{4\sqrt{2}}}}}\)
\(\left(\sqrt{3}-\sqrt{2}\right)\sqrt{5+2\sqrt{6}}\)
Tính:
a.\(A=\sqrt{4+\sqrt{6-2\sqrt{5}}}\)
b.\(B=\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)
c.\(C=\sqrt{6+2\sqrt{5}-\sqrt{29-12\sqrt{5}}}\)
d.\(D=2\sqrt{4-\sqrt{5+\sqrt{21+\sqrt{80}}}}\)
Giúp em với ạ!
Rút gọn
a, \(\sqrt{4+\sqrt{7+4\sqrt{3}}}\)
b, \(\sqrt{5+\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)
c, \(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)
d, \(\sqrt{x+2\sqrt{x}-1}\)+ \(\sqrt{x-2\sqrt{x-1}}\) ( x \(\ge\)0)
