\(=\sqrt{5-\sqrt{3-\sqrt{\left(2\sqrt{5}-3\right)^2}}}\)
\(=\sqrt{5-\sqrt{6-2\sqrt{5}}}\)
\(=\sqrt{5-\sqrt{\left(\sqrt{5}-1\right)^2}}\)
\(=\sqrt{6-\sqrt{5}}\)
Ko rút gọn được nữa
rút gọn
a, \(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
b\(\sqrt{3+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)
thankyou các bạn trước
c) \(\sqrt{5-\sqrt{13+4\sqrt{3}}}+\sqrt{3+\sqrt{13+4\sqrt{3}}}\)
d) \(\sqrt{\sqrt{5}-\sqrt{3}-\sqrt{29-12\sqrt{5}}}\)
Bài 1: Tính
\(\sqrt{3+2\sqrt{3}}-\sqrt{4-2\sqrt{3}}\\ \sqrt{12+6\sqrt{3}+\sqrt{12-6\sqrt{3}}}\\ \sqrt{9-4\sqrt{2}+\sqrt{9+4\sqrt{2}}}\)
\(\sqrt{\sqrt{2}+2+\sqrt{4+\sqrt{9-\sqrt{32}}}}\\ \sqrt{6+2\sqrt{5}-\sqrt{29+12\sqrt{5}}}\\ \sqrt{8+\sqrt{8}+\sqrt{20}+\sqrt{40}}-\sqrt{\sqrt{49}+\sqrt{40}}\\ \sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)
a, \(\sqrt{\sqrt{3}-\sqrt{1-\sqrt{21-12\sqrt{3}}}}\)
b,\(\sqrt{13+30\sqrt{2+\sqrt{9}+4\sqrt{2}}}\)
c,\(\sqrt{5}-\sqrt{3-\sqrt{29}-12\sqrt{5}}\)
ai giúp tui với
\(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
giải bài này hộ
Rút gọn
A=\(\sqrt{13+4\sqrt{10}}\)
B= \(\sqrt{46-6\sqrt{5}}-\sqrt{29-12\sqrt{5}}\)
C= \(\dfrac{1}{\sqrt{2}-\sqrt{3}}-\dfrac{1}{\sqrt{3}-\sqrt{5}}+\dfrac{1}{\sqrt{5}-\sqrt{7}}\)
Tính và rút gọn :
1) \(\sqrt{14+2\sqrt{33}}\)
2) \(\sqrt{29-12\sqrt{5}}\)
3) \(\sqrt{16+2\sqrt{55}}\)
4) \(\sqrt{13+4\sqrt{10}}\)
5) \(\sqrt{36+12\sqrt{5}}\)
6) \(\sqrt{21-6\sqrt{6}}\)
Câu1: Rút gọn
\(a,x+\sqrt{\left(x+2\right)^2}\cdot\left(x-2\right)\\ b,\sqrt{m^2-6m+9-2m}\left(x>3\right)\\ c,1+\sqrt{\frac{\left(x-1\right)^2}{x-1}}\\ d,\sqrt{x+4\sqrt{x-4}}+\sqrt{x-4\sqrt{x-4}}\)
Câu 2: So sánh
\(a,3và\sqrt{5}\\ \\ \\ b,2\sqrt{2}và3\sqrt{2}\\ \\ \\ c,-4\sqrt{5}và-6\sqrt{6}\\ \\ \\ d,2\sqrt{3}-5và\sqrt{3}-4\\ \\ \\e,A=\sqrt{2006}-\sqrt{2005}và\\ B=\sqrt{2005}-\sqrt{2004}\)
Câu 3: Rút gọn
\(a,\sqrt{16-2\sqrt{55}}\\ \\ \\ \\ \\ \\ \\ \\ \\ b,\sqrt{14-6\sqrt{5}}\\ \\ \\ \\ \\ \\ \\ \\ \\ c,\sqrt{36+12\sqrt{5}}\\ \\ \\ \\ \\ \\ \\ \\ \\ d,\sqrt{29+12\sqrt{5}}\)
Câu4: Tìm đkxđ
\(a,\sqrt{x^2-9}\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ b,\sqrt{x^2-3x+2}\)
\(c,\frac{\sqrt{x+3}}{\sqrt{5-x}}\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ d,\sqrt{\frac{x+3}{5-x}}\)
\(K=\left[\dfrac{x+3\sqrt{x}+2}{x+\sqrt{x}-2}-\dfrac{x+\sqrt{x}}{x-1}\right]:\left[\dfrac{1}{\sqrt{x}+1}+\dfrac{1}{\sqrt{x}-1}\right]\)
a,Rút gọn K
b,Tính K khi x=\(24+\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
c,Tìm x để \(\dfrac{1}{K}-\dfrac{\sqrt{x}+1}{8}\)≥1
