=\(\sqrt{2^2-2.2\sqrt{5}+\left(\sqrt{5}\right)^2}\)
=\(\sqrt{\left(2-\sqrt{5}\right)^2}\)
= \(2-\sqrt{5}\)
\(\sqrt{9-4\sqrt{5}}\)
\(=\sqrt{\left(\sqrt{5}\right)^2-2.\sqrt{5}.2+2^2}\)
\(=\sqrt{\left(\sqrt{5}-2\right)^2}=\sqrt{5}-2\)
Xin lỗi nick cuuar mình bị hack nhé mọi người
Ai mà bị chửi bới xúc phạm mong thông cảm ạ
Chứng minh:
\(\dfrac{a+\sqrt{2+\sqrt{5}}.\sqrt{\sqrt{9-4\sqrt{5}}}}{\sqrt[3]{2-\sqrt{5}}.\sqrt[3]{\sqrt{9+4\sqrt{5}}}-\sqrt[3]{a^2}+\sqrt[3]{a}}=-\sqrt[3]{a}-1\)
Rút gọn biểu thức:
a) \(\sqrt{8+4\sqrt{3}}-\sqrt{8-4\sqrt{3}}\)
b) \(\dfrac{\sqrt{21+8\sqrt{5}}}{4+\sqrt{5}}.\sqrt{9-4\sqrt{5}}\)
Rút gọn:
a) \(\sqrt{8+4\sqrt{3}}-\sqrt{8-4\sqrt{3}}\)
b) \(\sqrt{9-4\sqrt{5}}-\sqrt{9+4\sqrt{5}}\)
M=\(\sqrt{9+4\sqrt{5}}-\sqrt{6-2\sqrt{5}}\)
N=\(\sqrt{7-4\sqrt{3}}-\sqrt{12-6\sqrt{3}}\)
Tính (Rút gọn):
a) \(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
b)\(\sqrt{10+2\sqrt{6}+2\sqrt{10}+2\sqrt{15}}\)
c)\(\left(\sqrt{5+2\sqrt{9\sqrt{5}-19}}-\sqrt{7-\sqrt{5}}\right):2\sqrt{\sqrt{5}-2}\)
d)\(\frac{\sqrt{9+\sqrt{5}}+\sqrt{9-\sqrt{5}}}{\sqrt{9+2\sqrt{19}}}-\sqrt{3-2\sqrt{2}}\)
Tính
1/ \(\sqrt{17-4\sqrt{9+4\sqrt{5}}}\)
2/ \(\sqrt{17-6\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)
3/ \(\sqrt{3+\sqrt{5-\sqrt{13+4\sqrt{3}}}}\)
4/ \(\sqrt{27+10\sqrt{2}}:\dfrac{1}{\sqrt{\left(\sqrt{2}-5\right)^2}}\)
\(\sqrt{3-2\sqrt{2}}-\sqrt{11+6\sqrt{2}}\)
\(\sqrt{4-2\sqrt{3}}-\sqrt{7-4\sqrt{3}}+\sqrt{19+8\sqrt{3}}\)
\(\sqrt{6-2\sqrt{5}}+\sqrt{9+4\sqrt{5}}-\sqrt{14-6\sqrt{5}}\)
\(\sqrt{11-4\sqrt{7}}+\sqrt{23-8\sqrt{7}}+\sqrt{\left(-2^6\right)}\)
rút gọn:giải chi tiết hộ mình nha
Rút gọn các biểu thức sau:
\(a,\sqrt[3]{2+\sqrt{5}}+\sqrt[3]{2-\sqrt{5}}\)
\(b,\sqrt[3]{9+4\sqrt{5}}+\sqrt[3]{9-4\sqrt{5}}\)
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) \(\sqrt{9-\sqrt{5\sqrt{3}+5\sqrt{8+10\sqrt{7-4\sqrt{3}}}}}\)
Chứng minh :
a) \(9+4\sqrt{5}=\left(\sqrt{5}+2\right)^2\)
b) \(\sqrt{9-4\sqrt{5}}-\sqrt{5}\)
