CMR: \(4< \sqrt{6+\sqrt{6+...+\sqrt{6}}}+\sqrt[3]{6+\sqrt[3]{6+...+\sqrt[3]{6}}}< 5\)
CMR:\(4< \sqrt{6+\sqrt{6+...+\sqrt{6}}}+\sqrt[3]{6+\sqrt[3]{6+...+\sqrt[3]{6}}}< 5\)
Chứng minh rằng:
a)\(\frac{\left(5+2\sqrt{6}\right)\left(49-20\sqrt{6}\right)\left(\sqrt{5-2\sqrt{6}}\right)}{9\sqrt{3}-11\sqrt{2}}\) là số nguyên
b)\(\left(\sqrt{3}-1\right).\sqrt{6+2\sqrt{2}\sqrt{3-\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-\sqrt{128}}}}}\)
CHứng minh rằng: C=\(\sqrt{6+\sqrt{6+\sqrt{6+...+\sqrt{6}}}}< 3\)
Bài 1:
1.\(\sqrt{2-\sqrt{3}}\)
2.\(\sqrt{3+\sqrt{5}}\)
3.\(\sqrt{21-6\sqrt{6}}\)
4.\(\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}\)
5.\(\left(2-\sqrt{3}\right)\sqrt{7+4\sqrt{3}}\)
6.\(\sqrt{13+4\sqrt{10}}+\sqrt{13-4\sqrt{10}}\)
Tính:
a) \(\dfrac{\sqrt{7}-5}{2}-\dfrac{6-2\sqrt{7}}{4}+\dfrac{6}{\sqrt{7}-2}-\dfrac{5}{4+\sqrt{7}}\)
b) \(\dfrac{2}{\sqrt{6}-2}+\dfrac{2}{\sqrt{6}+2}+\dfrac{5}{\sqrt{6}}\)
c) \(\dfrac{1}{\sqrt{3}}+\dfrac{1}{3\sqrt{2}}+\dfrac{1}{\sqrt{3}}\sqrt{\dfrac{5}{12}-\dfrac{1}{\sqrt{6}}}\)
d) \(\dfrac{2\sqrt{3-\sqrt{3+\sqrt{13+\sqrt{48}}}}}{\sqrt{6}-\sqrt{2}}\)
Gỉai giúp mk vs
\(\sqrt{21-6\sqrt{6}}\)
\(\sqrt{14-6\sqrt{5}}+\sqrt{14+6\sqrt{5}}\)
\(\left(3-\sqrt{2}\right)\sqrt{7+4\sqrt{3}}\)
\(\sqrt{13+4\sqrt{10}}+\sqrt{13-4\sqrt{10}}\)
\(\sqrt{6}\left(\sqrt{26+15\sqrt{3}}+\sqrt{26-15\sqrt{3}}\right)\)
Bài 1. Tính
a) A= \(\left[\dfrac{6+\sqrt{20}}{3+\sqrt{5}}+\dfrac{\sqrt{14}-\sqrt{2}}{\sqrt{7}-1}\right]\) : (2+ \(\sqrt{2}\))
b) B= \(\sqrt{5-2\sqrt{6}}+\sqrt{5+2\sqrt{6}}-\dfrac{11}{2\sqrt{3}+1}\)
Bài 2.
Cho A= \(\left(\dfrac{\sqrt{2}+\sqrt{3}}{\sqrt{2}-\sqrt{3}}-\dfrac{\sqrt{2}-\sqrt{3}}{\sqrt{2}+\sqrt{3}}\right).\dfrac{\sqrt{3}-1}{3\sqrt{2}-\sqrt{6}}\)
Chứng minh A là số nguyên.
Chứng minh :
\(\sqrt{5\sqrt{5\sqrt{5...\sqrt{5}}}}+\sqrt{6+\sqrt{6+\sqrt{6+...+\sqrt{6}}}}< 8\)
(2018 dấu căn )
