\(\sqrt{2\sqrt{3\sqrt{4...\sqrt{1999\sqrt{2000}}}}}< \sqrt{2\sqrt{3\sqrt{4...\sqrt{1999.2001}}}}\)
\(< \sqrt{2\sqrt{3\sqrt{4...\sqrt{1998.2000}}}}< ...< \sqrt{2.4}< 3\)
CMR
\(\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+...+\frac{1}{\sqrt{2013^2-1}+\sqrt{2013^2}}=2012\)
\(\sqrt{x^2+\sqrt[3]{x^4y^2}}+\sqrt{y^2+\sqrt[3]{x^2y^4}}=a\)
CMR:\(\sqrt[3]{x^2}+\sqrt[3]{y^2}=\sqrt[3]{a^2}\)
Cmr:
\(\sqrt[3]{\sqrt[3]{2}-1}=\sqrt[3]{\dfrac{1}{9}}-\sqrt[3]{\dfrac{2}{9}}+\sqrt[3]{\dfrac{4}{9}}\)
I : Tính
\(D=\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+......+\frac{1}{\sqrt{1999}+\sqrt{2000}}\)
help me !!!
CMR:
\(\dfrac{1}{2\sqrt{1}+1\sqrt{2}}+\dfrac{1}{3\sqrt{2}+2\sqrt{3}}+\dfrac{1}{4\sqrt{3}+3\sqrt{3}}+....+\dfrac{1}{\left(n+1\right)\left(\sqrt{n}+n\sqrt{n+1}\right)}< 1\)
CMR nếu : \(\sqrt{x^2+\sqrt[3]{x^4y^2}}+\sqrt{y^2+\sqrt[3]{x^2y^4}}=a\)
thì \(\sqrt[3]{x^2}+\sqrt[3]{y^2}=\sqrt[3]{a^2}\)
Bài 1: CMR các biểu thức sau là một số nguyên
a)A=\(\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)
b)\(B=\left(\sqrt{3}-1\right)\sqrt{6+2\sqrt{21}\sqrt{3-\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18}-\sqrt{128}}}}\)
CMR \(\sin22,\:5^0=\frac{\sqrt{3+\sqrt{2}}}{\sqrt{4+2\sqrt{2}}}\)
CMR: \(\dfrac{4}{\sqrt{5}-1}+\dfrac{3}{\sqrt{5}-2}+\dfrac{16}{\sqrt{5}-3}=-5\)
