\(\sqrt{19}-\sqrt{17}=\dfrac{2}{\sqrt{19}+\sqrt{17}}\)
\(\sqrt{21}-\sqrt{19}=\dfrac{2}{\sqrt{21}+\sqrt{19}}\)
mà \(\sqrt{17}+\sqrt{19}< \sqrt{21}+\sqrt{19}\)
nên \(\sqrt{19}-\sqrt{17}>\sqrt{21}-\sqrt{19}\)
So sánh 2 số sau:
\(a,\frac{23-2\sqrt{19}}{3}\) và \(\sqrt{27}\)
\(b,\sqrt{17}+\sqrt{19}\) và 9
\(\left(\sqrt{3}+4\right)\sqrt{19-8\sqrt{3}}+\left(\sqrt{3}-4\right)\sqrt{19+8\sqrt{3}}\)
\(\left(\sqrt{\left(\sqrt{20}\right)-\sqrt{19}}\right)^x+\left(\sqrt{\left(\sqrt{20}\right)+\sqrt{19}}\right)^x=2\)
I : Rút gọn
\(A=\sqrt{7-4\sqrt{3}}\)
\(B=\sqrt{19-8\sqrt{3}}\)
\(C=\sqrt{21-4\sqrt{5}}\)
\(D=\left(4+\sqrt{15}\right)\left(\sqrt{5}-\sqrt{3}\right)\sqrt{8-2\sqrt{5}}\)
help me !!!
1. So sánh:
a. \(\sqrt{18}+\sqrt{19}\) và 9
b. \(\frac{16}{\sqrt{2}}\)và \(\sqrt{5}.\sqrt{25}\)
2. Cho Hđt \(\sqrt{a\pm\sqrt{b}}=\sqrt{\frac{a+\sqrt{a^2-b}}{2}}\pm\sqrt{\frac{a-\sqrt{a^2-b}}{2}}\)vs \(\left(a,b>0,a^2-b>0\right)\)
Áp dụng kết quả để rút gọn:
a. \(\frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
b. \(\frac{\sqrt{3-2\sqrt{2}}}{\sqrt{17-12\sqrt{2}}}-\frac{\sqrt{3+2\sqrt{2}}}{\sqrt{17+12\sqrt{2}}}\)
c. \(\sqrt{\frac{2\sqrt{10}+\sqrt{30}-2\sqrt{2}-\sqrt{6}}{2\sqrt{10}-2\sqrt{2}}}:\frac{2}{\sqrt{3}-1}\)
So sánh \(\sqrt{2015}+\sqrt{2018}\) và \(\sqrt{2016}+\sqrt{2017}\)
So sánh:
\(a,\sqrt{n-1}+\sqrt{n+1}\) và \(2\sqrt{n}\) ( với n ≥ 1 )
b, \(A=2\sqrt{1}+2\sqrt{3}+2\sqrt{5}+...+2\sqrt{19}\)
và \(B=2\sqrt{2}+2\sqrt{4}+...+2\sqrt{18}+\sqrt{20}\)
So sánh 2 số: \(R=\dfrac{3+\sqrt{5}}{2\sqrt{2}+\sqrt{3+\sqrt{5}}}+\dfrac{3-\sqrt{5}}{2\sqrt{2}-\sqrt{3-\sqrt{5}}}\)
\(S=\dfrac{4+\sqrt{7}}{3\sqrt{2}+\sqrt{4+\sqrt{7}}}+\dfrac{4-\sqrt{7}}{3\sqrt{2}-\sqrt{4-\sqrt{7}}}\)
So sánh 2 số: \(R=\dfrac{3+\sqrt{5}}{2\sqrt{2}+\sqrt{3+\sqrt{5}}}+\dfrac{3-\sqrt{5}}{2\sqrt{2}-\sqrt{3-\sqrt{5}}}\)
\(S=\dfrac{4+\sqrt{7}}{3\sqrt{2}+\sqrt{4+\sqrt{7}}}+\dfrac{4-\sqrt{7}}{2\sqrt{2}-\sqrt{3-\sqrt{5}}}\)
