Ta có: \(\sqrt{11-2\sqrt{30}}\)
\(=\sqrt{6-2\cdot\sqrt{6}\cdot\sqrt{5}+5}\)
\(=\sqrt{\left(\sqrt{6}-\sqrt{5}\right)^2}\)
\(=\left|\sqrt{6}-\sqrt{5}\right|=\sqrt{6}-\sqrt{5}\)
Câu 1: Tính
a. \(\sqrt{3\dfrac{6}{25}}\) b. \(\sqrt[3]{261}\) c. \(\sqrt{8,1}\) . \(\sqrt{20}\). \(\sqrt{8}\)
d. \(\sqrt{11+2\sqrt{30}}-\sqrt{11-2\sqrt{30}}\)
tinh gia tri bieu thut :\(\sqrt{11-2\sqrt{30}}-\sqrt{11+2\sqrt{30}}\)
\(\left(\sqrt{11}-\sqrt{3}\right)\left(\sqrt{13-\sqrt{6}+2\sqrt{30-\sqrt{54}}}+\sqrt{11}-\sqrt{10-\sqrt{6}}\right)\)
RÚT GỌN
Rút gọn:
A = \(\left(\sqrt{11}-\sqrt{3}\right)\left(\sqrt{13-\sqrt{6}+2\sqrt{30-\sqrt{54}}}+\sqrt{11}-\sqrt{10-\sqrt{6}}\right)\)
Rút gọn
\(\dfrac{1}{\sqrt{11-2\sqrt{30}}}-\dfrac{3}{7-2\sqrt{10}}\)
\(A=\left(\sqrt{22}+7\sqrt{2}\right)\sqrt{30-7\sqrt{11}}\)
rút gọn
\(C=\left(\sqrt{11+2\sqrt{30}}-\sqrt{8-4\sqrt{3}}\right)\left(\sqrt{5}+\sqrt{2}\right)\)
Tính: \(\left(\sqrt{22}+7\sqrt{2}\right)\sqrt{30-7\sqrt{11}}\)
Rút gọn
1) \(E=\left(\sqrt{11}-3\right)\left(\sqrt{13-\sqrt{6}+2\sqrt{30-\sqrt{54}}}+\sqrt{11}-\sqrt{10-\sqrt{6}}\right)\)
2) \(F=\frac{\left(\sqrt{3-\sqrt{5}}-1\right)\left(\sqrt{3-\sqrt{5}}\left(3-\sqrt{5}\right)+1\right)}{4-\sqrt{5}-\sqrt{3-\sqrt{5}}}+\sqrt{5}\)
TÍNH:
\(\left(\sqrt{22}+7\sqrt{2}\right)\sqrt{30-7\sqrt{11}}\)
