\(\left(\sqrt{5}+\sqrt{2}\right)\left(3\sqrt{2}-1\right)=3\sqrt{10}-\sqrt{5}+6-\sqrt{2}\)
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Tính
a) \(\left(2-\sqrt{3}\right)\cdot\left(2+\sqrt{3}\right)\)
b) \(\left(2\sqrt{3}-\sqrt{5}\right)\cdot\left(2\sqrt{3}+\sqrt{5}\right)\)
\(\left(\sqrt{2}+1\right)\cdot\left(\sqrt{3}+1\right)\cdot\left(\sqrt{6}+1\right)\cdot\left(5-2\sqrt{2}-\sqrt{3}\right)\)
Giúp mình giải bài trên với ạ. Cần gấp. Đầu bài yêu cầu: Tính
1) frac{3+2sqrt{3}}{sqrt{3}}+frac{2+sqrt{2}}{sqrt{2}+1}-left(sqrt{2}+3right)2) 0.1sqrt{left(-3right)^2}cdotleft[6sqrt{left(-frac{1}{3}right)^2}-sqrt{left(sqrt{3}-2right)^2}right]^23) left(frac{3+2sqrt{3}}{sqrt{3}+2}+frac{2+sqrt{2}}{sqrt{2}+1}right)divleft(1divfrac{1}{sqrt{2}+sqrt{3}}right)4) left(frac{3sqrt{2}+sqrt{6}}{sqrt{12}+2}-frac{sqrt{54}}{3}right)cdotfrac{2}{sqrt{6}}5) sqrt{frac{5+2sqrt{6}}{5-2sqrt{6}}}+sqrt{frac{5-2sqrt{6}}{5+2sqrt{6}}}
Đọc tiếp
1) \(\frac{3+2\sqrt{3}}{\sqrt{3}}+\frac{2+\sqrt{2}}{\sqrt{2}+1}-\left(\sqrt{2}+3\right)\)
2) \(0.1\sqrt{\left(-3\right)^2}\cdot\left[6\sqrt{\left(-\frac{1}{3}\right)^2}-\sqrt{\left(\sqrt{3}-2\right)^2}\right]^2\)
3) \(\left(\frac{3+2\sqrt{3}}{\sqrt{3}+2}+\frac{2+\sqrt{2}}{\sqrt{2}+1}\right)\div\left(1\div\frac{1}{\sqrt{2}+\sqrt{3}}\right)\)
4) \(\left(\frac{3\sqrt{2}+\sqrt{6}}{\sqrt{12}+2}-\frac{\sqrt{54}}{3}\right)\cdot\frac{2}{\sqrt{6}}\)
5) \(\sqrt{\frac{5+2\sqrt{6}}{5-2\sqrt{6}}}+\sqrt{\frac{5-2\sqrt{6}}{5+2\sqrt{6}}}\)
TÍNH :Asqrt{3+sqrt{5+2sqrt{3}}}cdotsqrt{3-sqrt{5+2sqrt{3}}}Bsqrt{4+sqrt{8}}cdotsqrt{2+sqrt{2+sqrt{2}}}cdotsqrt{2-sqrt{2+sqrt{2}}}Csqrt{2+sqrt{3}}cdotsqrt{2+sqrt{2+sqrt{3}}}cdotsqrt{2+sqrt{2+sqrt{2+sqrt{3}}}}cdotsqrt{2-sqrt{2+sqrt{2+sqrt{3}}}}Dleft[4+sqrt{15}right]left[sqrt{10}-sqrt{6}right]cdotsqrt{4-sqrt{15}}Eleft[3-sqrt{5}right]cdotsqrt{3+sqrt{5}}text{ }+left[3+sqrt{5}right]cdotsqrt{3-sqrt{5}}
Đọc tiếp
TÍNH :
\(A=\sqrt{3+\sqrt{5+2\sqrt{3}}}\cdot\sqrt{3-\sqrt{5+2\sqrt{3}}}\)
\(B=\sqrt{4+\sqrt{8}}\cdot\sqrt{2+\sqrt{2+\sqrt{2}}}\cdot\sqrt{2-\sqrt{2+\sqrt{2}}}\)
\(C=\sqrt{2+\sqrt{3}}\cdot\sqrt{2+\sqrt{2+\sqrt{3}}}\cdot\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}\cdot\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}\)
\(D=\left[4+\sqrt{15}\right]\left[\sqrt{10}-\sqrt{6}\right]\cdot\sqrt{4-\sqrt{15}}\)
\(E=\left[3-\sqrt{5}\right]\cdot\sqrt{3+\sqrt{5}}\text{ }+\left[3+\sqrt{5}\right]\cdot\sqrt{3-\sqrt{5}}\)
tính B=\(\sqrt{3\cdot\sqrt{5}}\cdot\left(3+\sqrt{5}\right)\cdot\left(\sqrt{10}-\sqrt{2}\right)\)
Chứng minh: \(\frac{1}{2\cdot\sqrt{1}}+\frac{1}{3\cdot\sqrt{2}}+\frac{1}{4\cdot\sqrt{3}}+...+\frac{1}{2012\cdot\sqrt{2011}}+\frac{1}{2013\cdot\sqrt{2012}}\)\(< 2\)
Chứng minh: A=\(\frac{1}{3\cdot\left(\sqrt{1}+\sqrt{2}\right)}+\frac{1}{5\cdot\left(\sqrt{2}+\sqrt{3}\right)}+...+\frac{1}{97\cdot\left(\sqrt{48}+\sqrt{49}\right)}\)\(< \frac{1}{2}\)
\(\sqrt{3-\sqrt{5}}\cdot\left(\sqrt{10}-\sqrt{2}\right)\cdot\left(3+\sqrt{5}\right)\)
Tính giá trị của biểu thức:
N=\(\dfrac{\sqrt{1+\sqrt{1-x^2}}\cdot\left(\sqrt{\left(1+x\right)^3}-\sqrt{\left(1-x\right)^3}\right)}{2+\sqrt{1-x^2}}\)
Tại x =\(\dfrac{1}{5}\)
Tính
A=\(\left(\frac{15}{\sqrt{7}+2}+\frac{12}{\sqrt{7}-1}-\frac{8}{3-\sqrt{7}}\right)\cdot\left(3\sqrt{7}+20\right)\)
B=\(\left(9+4\sqrt{5}\right):\left(\frac{\sqrt{5}+2}{\sqrt{5}-2}\right)\)
a) \(\left(2+\sqrt{3}\right)\cdot\sqrt{7-4\sqrt{3}}\)
b) \(\sqrt{4+2\sqrt{3}}-\sqrt{5+2\sqrt{6}}+\sqrt{2}+\sqrt{9-4\sqrt{5}}-\sqrt{9+4\sqrt{5}}\)
c) \(\sqrt{3-\sqrt{5}}\cdot\left(\sqrt{10}-\sqrt{2}\right)\left(3+\sqrt{5}\right)\)