a. \(\sqrt{13}+3>\sqrt{11}+2\sqrt{2}\) ( 3 > 2\(\sqrt{2}\) )
b. \(\sqrt{13}-\sqrt{11}-\left(\sqrt{7}-\sqrt{5}\right)\) = \(\dfrac{2}{\sqrt{13}+\sqrt{11}}-\dfrac{2}{\sqrt{7}+\sqrt{5}}< 0\)
\(\Rightarrow\sqrt{13}+\sqrt{5}< \sqrt{11}+\sqrt{7}\)
Tính
a/ \(2\sqrt{\dfrac{9-\sqrt{77}}{2}}-\sqrt{\dfrac{2}{10-3\sqrt{11}}}\)
b/ \(\left(\sqrt{13}-1\right)\sqrt{\dfrac{2}{7-\sqrt{13}}}+\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
Tính \(\left(\sqrt{7}+\sqrt{11}+\sqrt{13}\right)\left(\sqrt{11}+\sqrt{13}-\sqrt{7}\right)\left(\sqrt{7}+\sqrt{13}-\sqrt{11}\right)\left(\sqrt{7}+\sqrt{11}-\sqrt{13}\right)\)
\(a,\frac{2}{\sqrt{13}-\sqrt{11}}+\frac{5}{4+\sqrt{ }11}-\sqrt{52}
\)
b,\(\sqrt{6+2\sqrt{5}+\sqrt{9-4\sqrt{5}}-\sqrt{20}}\)
1/Tính
A=\(\dfrac{\sqrt{15-10\sqrt{2}}+\sqrt{13+4\sqrt{10}}-\sqrt{11+2\sqrt{10}}}{2\sqrt{3+2\sqrt{2}}+\sqrt{9-4\sqrt{2}}+\sqrt{12+8\sqrt{2}}}\)
B=\(\dfrac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2}+\sqrt{3}}+\dfrac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2}-\sqrt{3}}\)
C=\(\dfrac{\sqrt{2-\sqrt{3}}+\sqrt{4-\sqrt{15}}+\sqrt{10}}{\sqrt{23-3\sqrt{5}}}\)
D=\(\dfrac{\sqrt{4+\sqrt{3}}+\sqrt{4-\sqrt{3}}}{\sqrt{4+\sqrt{13}}}\)
2/So sánh
\(\sqrt{2017^2-1}-\sqrt{2016^2-1}\) và \(\dfrac{2.1016}{\sqrt{2017^2-1}+\sqrt{2016^2-1}}\)
Rút gọn
\(C=\left(\sqrt{12+2\sqrt{14+2\sqrt{13}}}-\sqrt{12+2\sqrt{11}}\right)\left(\sqrt{11}+\sqrt{13}\right)\)
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.\(\sqrt{13+4\sqrt{10}}+\sqrt{13-4\sqrt{10}}\)
Bài 1:
a) \(\sqrt{13-2\sqrt{42}}\)
b) \(\sqrt{46+6\sqrt{5}}\)
c) \(\sqrt{12-3\sqrt{15}}\)
d) \(\sqrt{11+\sqrt{96}}\)
Bài 2:
a) \(A=\sqrt{6+2\sqrt{2}\sqrt{3-\sqrt{4+2\sqrt{3}}}}\)
b) \(B=\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}\)
c) \(C=\sqrt{3-\sqrt{5}}\left(\sqrt{10}+\sqrt{2}\right)\left(3+\sqrt{5}\right)\)
d) \(D=\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}\)
e) \(E=\sqrt{8+2\sqrt{10+2\sqrt{5}}}+\sqrt{8-2\sqrt{10+2\sqrt{5}}}\)
g) \(G=\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}\)
h) \(H=4x-\sqrt{9x^2-12x+4}\)
i) \(\frac{\sqrt{7}-\sqrt{2}}{\sqrt{7}+\sqrt{2}}+\frac{\sqrt{7}+\sqrt{2}}{\sqrt{7}-\sqrt{2}}\)
Thực hiện phép tính:
a)\(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)
b)\(\left(\sqrt{3}-\sqrt{2}\right)\sqrt{5+2\sqrt{6}}\)
c)\(\sqrt{5-\sqrt{13+4\sqrt{3}}}+\sqrt{3+\sqrt{13+4\sqrt{3}}}\)
d)\(\sqrt{1+\sqrt{3+\sqrt{13+4\sqrt{3}}}}+\sqrt{1-\sqrt{3-\sqrt{13-4\sqrt{3}}}}\)
Mọi người giải gấp giúp em với!!!!
Bài 1:Tính
1.\(\sqrt{12,5}\cdot\sqrt{0,2}\cdot\sqrt{0,1}\)
2.\(\sqrt{48,4}\cdot\sqrt{5}\cdot\sqrt{0,5}\)
Bài 2:Khai triển các hằng đẳng thức sau:
a,\(\left(\sqrt{7}+\sqrt{3}\right)^2\)
b,\(\left(\sqrt{11}-\sqrt{5}\right)^2\)
c,\(\left(\sqrt{x}+\sqrt{y}\right)^2\)
d,\(\left(\sqrt{13}+\sqrt{7}\right)^2\)
e,\(\left(\sqrt{a}-\sqrt{b}\right)^2\)
f,\(\left(\sqrt{3}-1\right)^2\)
so sánh
2 và \(\sqrt{2}\)+ 1
2\(\sqrt{31}\)và 10
\(-3\sqrt{11}\)và - \(\sqrt{12}\)
