\(A=\sqrt{4-\sqrt{10-2\sqrt{5}}}-\sqrt{4+\sqrt{10-2\sqrt{5}}}\)
\(A^2=8-2\sqrt{\left(4-\sqrt{10-2\sqrt{5}}\right)\left(4+\sqrt{10-2\sqrt{5}}\right)}\)
\(A^2=8-2\sqrt{5+2\sqrt{5}+1}\)
\(A^2=8-2\sqrt{5}-2\)
\(A^2=5-2\sqrt{5}+1\)
\(A=1-\sqrt{5}\left(A< 0\right)\)
Bài 1: Tính
1, \(A=\left(1-\frac{5+\sqrt{5}}{1+\sqrt{5}}\right).\left(\frac{5-\sqrt{5}}{1-\sqrt{5}}-1\right)\)
2, \(B=\left(\frac{3\sqrt{125}}{15}-\frac{10-4\sqrt{6}}{\sqrt{5}-2}\right).\frac{1}{\sqrt{5}}\)
3, \(C=\left(\frac{\sqrt{1000}}{100}-\frac{5\sqrt{2}-2\sqrt{5}}{2\sqrt{5}-8}\right).\frac{\sqrt{10}}{10}\)
4, \(D=\frac{1}{\sqrt{49+20\sqrt{6}}}-\frac{1}{\sqrt{49-20\sqrt{6}}}+\frac{1}{\sqrt{7-4\sqrt{3}}}\)
5, \(E=\frac{1}{\sqrt{4-2\sqrt{3}}}-\frac{1}{\sqrt{7-\sqrt{48}}}+\frac{3}{\sqrt{14-6\sqrt{5}}}\)
6, \(F=\frac{1}{\sqrt{2}-\sqrt{3}}\sqrt{\frac{3\sqrt{2}-2\sqrt{3}}{3\sqrt{2}+2\sqrt{3}}}\)
7, \(G=\frac{\sqrt{15-10\sqrt{2}}+\sqrt{13+4\sqrt{10}-\sqrt{11-2\sqrt{10}}}}{2\sqrt{3+2\sqrt{2}}+\sqrt{9-4\sqrt{2}+\sqrt{12+8\sqrt{2}}}}\)
Câu 1: Rút gọn:
a) \(2\sqrt{18}-4\sqrt{50}-3\sqrt{32}\)
b) \(\sqrt{14-6\sqrt{5}}+\sqrt{6+2\sqrt{5}}\)
c) \(\dfrac{\sqrt{10}+10}{1+\sqrt{10}}-\dfrac{5\sqrt{2}-2\sqrt{5}}{\sqrt{5}-\sqrt{2}}\)
Câu 2: Giải phương trình:
\(\sqrt{9x^2-30x+25}=5\)
\(C=\dfrac{\sqrt{15-10\sqrt{2}}+\sqrt{13+4\sqrt{10}}-\sqrt{11+2\sqrt{10}}}{2\sqrt{3+2\sqrt{2}}+\sqrt{9-4\sqrt{2}}+\sqrt{12+8\sqrt{2}}}\)
\(B=\dfrac{20}{3+\sqrt{5}+\sqrt{2+2\sqrt{5}}}\)
Rút gọn
A= \(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
B= \(\sqrt{4+\sqrt{15}}+\sqrt{4-\sqrt{15}}-2\sqrt{3-5}\)
\(A=\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
C=\(\sqrt{4+\sqrt{10+2\sqrt{5}}}-\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
Tính B=\(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10-2\sqrt{5}}}\)
C= \(\sqrt{5\sqrt{9}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)
D= \(\sqrt{x+2\sqrt{2x+4}}+\sqrt{x-2\sqrt{2x-4}}\)
# Các bạn giúp mình với ạ :<<
a) \(\sqrt{8-4\sqrt{3}}-\sqrt{8+4\sqrt{3}}\)
b) \(\sqrt{9-\sqrt{5\sqrt{3}+5\sqrt{8+10\sqrt{7-4\sqrt{3}}}}}\)
c) \(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
Dạng bài này mk chưa quen lắm mong mn giúp :)
Tính:
a) \(\sqrt{\sqrt{5}-2}-\sqrt{5\sqrt{5}+10}+\sqrt{4\sqrt{5}+8}\)
b) \(\sqrt{\sqrt{2}-1}+\sqrt{\sqrt{2}+1}-\sqrt{2\sqrt{2}+2}\)
