\(\frac{11}{4-\sqrt{5}}+\frac{4}{3-\sqrt{5}}-\frac{19}{\sqrt{21+4\sqrt{5}}}=\frac{11\left(4+\sqrt{5}\right)}{16-5}+\frac{4\left(3+\sqrt{5}\right)}{9-5}-\frac{19}{\sqrt{\left(2\sqrt{5}\right)^2+2.2\sqrt{5}+1}}\)
\(=4+\sqrt{5}+3+\sqrt{5}-\frac{19}{\sqrt{\left(2\sqrt{5}+1\right)^2}}=7+2\sqrt{5}-\frac{19}{2\sqrt{5}+1}\)
\(=7+2\sqrt{5}-\frac{19\left(2\sqrt{5}-1\right)}{20-1}=7+2\sqrt{5}-\left(2\sqrt{5}-1\right)=8\)
Bài 1. thực hiện phép tính
a) \(\sqrt{\frac{5+\sqrt{21}}{5-\sqrt{21}}}+\sqrt{\frac{5-\sqrt{21}}{5+\sqrt{21}}}\) b) \(\sqrt{\frac{4+\sqrt{7}}{4-\sqrt{7}}}+\sqrt{\frac{4-\sqrt{7}}{4+\sqrt{7}}}\)
Bài 2. Tính:a) \(M=\left(2\sqrt{2}\right)\sqrt{2+4\sqrt{3+\sqrt{2}+\sqrt{11-6\sqrt{2}}}}\)
b) \(\frac{1}{\sqrt{25}+\sqrt{24}}+\frac{1}{\sqrt{24}+\sqrt{23}}+...+\frac{1}{\sqrt{2}+\sqrt{1}}=4\)
c)
\(\frac{\left(5\sqrt{3}+\sqrt{50}\right)\left(5-\sqrt{24}\right)}{\sqrt{75}0-5\sqrt{2}}\)
\(\sqrt{\frac{9-4\cdot\sqrt{3}}{6+\sqrt{3}}}-\sqrt{\frac{3+4\cdot\sqrt{3}}{5\sqrt{3}-6}}\)
\(\frac{5+\sqrt{5}}{\sqrt{5}+2}+\frac{\sqrt{5}-5}{\sqrt{5}}-\frac{11}{2\sqrt{5}+3}\)
RÚT GỌN
A.\(\sqrt{\frac{3\sqrt{3}-4}{2\sqrt{3}+1}+\sqrt{\frac{\sqrt{3}+4}{5-2\sqrt{3}}}}\)
B.\(\frac{\sqrt{4}+\sqrt{5}+\sqrt{4+5}}{\sqrt{4+\sqrt{11}}}\)
\(Tính\)
\(a.\left(\sqrt{10}-\sqrt{2}\right)\left(3+\sqrt{5}\right)\sqrt{27-9\sqrt{5}}\)
\(b.\sqrt{\frac{3\sqrt{3}-4}{2\sqrt{3}+1}}-\sqrt{\frac{4+\sqrt{3}}{5-2\sqrt{3}}}\)
\(c.\frac{3-4\sqrt{3}}{\sqrt{6}-\sqrt{2}-\sqrt{5}}\)
\(d.\left(\sqrt{11}-\sqrt{3}\right)\left(\sqrt{13-\sqrt{6}+2\sqrt{30-\sqrt{45}}}+\sqrt{11}-\sqrt{10-\sqrt{6}}\right)\)
\(e.\frac{\sqrt{4+\sqrt{5}}+\sqrt{4-\sqrt{5}}}{\sqrt{4}+\sqrt{11}}-\frac{\sqrt{20-4\sqrt{23}}}{\sqrt{5+\sqrt{2}}-\sqrt{5-\sqrt{2}}}\)
Thu gọn biểu thức
\(y=\frac{\sqrt{4+\sqrt{5}}+\sqrt{4-\sqrt{5}}}{\sqrt{4+\sqrt{11}}}-\frac{\sqrt{20-4\sqrt{23}}}{\sqrt{5+\sqrt{2}}-\sqrt{5-\sqrt{2}}}+\frac{8}{3+\sqrt{5}}\)
a) \(\frac{2\sqrt{5}-4\sqrt{10}}{3\sqrt{10}}\)
b)\(\frac{6\sqrt{6}-2\sqrt{12}+3-\sqrt{2}}{2\sqrt{6}+1}\)
c)\(\frac{\sqrt{3\left(3-\sqrt{11}\right)^2}}{\sqrt{6}\left(3-\sqrt{11}\right)}\)
d)\(\frac{5\sqrt{7}-4\sqrt{35}+7\sqrt{5}}{\sqrt{35}}\)
e) \(\left(\sqrt{3}-1\right)\sqrt{2\sqrt{19+8\sqrt{3}-4}}\)
g) \(\sqrt{47+\sqrt{5}}.\sqrt{7-\sqrt{2+\sqrt{5}}.}\sqrt{7+\sqrt{2+\sqrt{5}}}\)
1) Rút gọn biểu thức:
a) \(\frac{1}{7+4\sqrt{3}}+\frac{1}{7-4\sqrt{3}}\)
b) \(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6}-2}-\frac{12}{3-\sqrt{6}}-\sqrt{6}\)
c) \(\frac{5}{4-\sqrt{11}}+\frac{1}{3+\sqrt{7}}-\frac{6}{\sqrt{7}-2}-\frac{\sqrt{7}-5}{2}\)
d) \(\frac{4}{\sqrt{5}-\sqrt{2}}+\frac{3}{\sqrt{5}-2}-\frac{2}{\sqrt{3}-2}+\frac{\sqrt{3}-1}{6}\)
Toán số 9, liên quan đến dạng căn. Các bạn giúp mình nhé, xin cảm ơn rất nhiều. :)
1) \(\left(\sqrt{3-2\sqrt{\sqrt{3}-1}}+\frac{\sqrt{3}-1}{\sqrt{2}}\right)\sqrt{\sqrt{3}-1}\)
2) \(\left(\sqrt{5+2\sqrt{9\sqrt{5}-19}}-\sqrt{7-\sqrt{5}}\right):2\sqrt{\sqrt{5}-2}\)
3) \(\frac{\sqrt{10+6\sqrt{2}}-\sqrt{10-6\sqrt{2}}}{\sqrt{5-\sqrt{7}}}-\sqrt{9+2\sqrt{20}}\)
4) \(\frac{\sqrt{5+\sqrt{3}}+\sqrt{5-\sqrt{3}}}{\sqrt{5+\sqrt{22}}}-\frac{\sqrt{6-\sqrt{24}}}{\sqrt{3+\sqrt{3}}-\sqrt{3-\sqrt{3}}}\)
5) \(\sqrt{5+2\sqrt{14\sqrt{5}-26}}-\sqrt{4\sqrt{5}-1+\sqrt{80-8\sqrt{5}}}\)
6) \(\frac{\sqrt{11+\sqrt{5}}+\sqrt{11-\sqrt{5}}}{\sqrt{11+2\sqrt{29}}}-\sqrt{3-2\sqrt{2}}\)
\(K=\frac{\sqrt{4+\sqrt{5}}+\sqrt{4-\sqrt{5}}}{\sqrt{4+\sqrt{11}}}-\sqrt{9-4\sqrt{5}}-\frac{4}{\sqrt{5}-1}\)
TÍNH
