\(\left(5+2\sqrt{3}\right)\cdot\sqrt{37-20\sqrt{3}}\\ =\left(5+2\sqrt{3}\right)\cdot\sqrt{25-2\cdot10\sqrt{3}+12}\\ =\left(5+2\sqrt{3}\right)\cdot\sqrt{5^2-2\cdot5\cdot2\sqrt{3}+\left(2\sqrt{3}\right)^2}\\ =\left(5+2\sqrt{3}\right)\cdot\sqrt{\left(5-2\sqrt{3}\right)^2}\\ =\left(5+2\sqrt{3}\right)\left(5-2\sqrt{3}\right)\\ =5^2-\left(2\sqrt{3}\right)^2\\ =25-12=13\)
Tính: a. \(\left(3\sqrt{2}+\sqrt{6}\right)\cdot\left(6-3\sqrt{3}\right)\)
b. \(\left(4+\sqrt{15}\right)\cdot\left(\sqrt{10}-\sqrt{6}\right)\cdot\sqrt{4-\sqrt{15}}\)
c. \(\left(3-\sqrt{5}\right)\cdot\left(10-\sqrt{2}\right)\cdot\sqrt{3+\sqrt{5}}\)
\(A=\dfrac{1}{\sqrt{8}+\sqrt{7}}+\sqrt{175}+2\sqrt{2}\\ B=\left(5+2\sqrt{6}\right)\cdot\left(49-20\sqrt{6}\right)\cdot\sqrt{5-2\sqrt{6}}\)
\(C=\dfrac{1}{2}\left(\sqrt{6}+\sqrt{5}\right)^2-\dfrac{1}{4}\sqrt{120}-\sqrt{\dfrac{15}{2}}\)
\(D=\left(2\sqrt{6}-4\sqrt{3}+5\sqrt{2}+\dfrac{1}{4}\sqrt{8}\right)\cdot3\sqrt{6}\)
\(\frac{3+2\sqrt{3}}{\sqrt{3}}+\frac{2+\sqrt{2}}{\sqrt{2}+1}-\left(\sqrt{2}+3\right)\)
\(0.1\cdot\sqrt{\left(-3\right)^2}\cdot\left[6\sqrt{\left(\frac{1}{3}\right)^2}-\sqrt{\left(\sqrt{3}-2\right)^2}\right]^2\)
\(\left(\frac{3\sqrt{2}+\sqrt{6}}{\sqrt{12}+2}-\frac{\sqrt{54}}{3}\right)\cdot\frac{2}{\sqrt{6}}\)
\(\left(\frac{3+2\sqrt{3}}{\sqrt{3}+2}+\frac{2+\sqrt{2}}{\sqrt{2}+1}\right)\div\left(1\div\frac{1}{\sqrt{2}+\sqrt{3}}\right)\)
\(\sqrt{\frac{5+2\sqrt{6}}{5-2\sqrt{6}}}+\sqrt{\frac{5-2\sqrt{6}}{5+2\sqrt{6}}}\)
\(\left(\sqrt{6}+\sqrt{2}\right)\cdot\left(\sqrt{3}-\sqrt{2}\right)\cdot\sqrt{2+\sqrt{3}}\)
Thực hiện phép tính:\(\sqrt{3-\sqrt{5}}\cdot\left(3+\sqrt{5}\right)\cdot\left(\sqrt{10}-\sqrt{12}\right)\)
(\(\left(\sqrt{12}-6\sqrt{3}+\sqrt{24}\right)\cdot\sqrt{6}-\left(5\sqrt{\dfrac{1}{2}}+12\right)=-14.5\sqrt{2}\)
So sánh hai số A,B biết \(A=\sqrt{2+\sqrt{3}}\cdot\sqrt{2+\sqrt{2+\sqrt{3}}}\cdot\sqrt{2-\sqrt{2+\sqrt{3}}}\)
\(B=\left(\frac{1}{\sqrt{\sqrt{5}+2}}+\sqrt{\sqrt{5}+2}\right)\cdot\frac{1}{\sqrt{\sqrt{5}+1}}-\sqrt{3-2\sqrt{2}}\)
Mình cần gấp nha mng
Tính: a. \(\left(\sqrt{10}+\sqrt{2}\right)\cdot\left(6-2\sqrt{5}\right)\cdot\sqrt{3+\sqrt{5}}\)
b. \(\sqrt{3+\sqrt{5}}-\sqrt{3-\sqrt{5}}-\sqrt{2}\)
c. \(\sqrt{3,5-\sqrt{6}}+\sqrt{3,5+\sqrt{6}}\)
d, \(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}+\sqrt{7}\)
e, \(\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}-\sqrt{2}\)
Tính:
a)\(\sqrt{3\sqrt{2}-2\sqrt{3}}\cdot\sqrt{3\sqrt{2}+2\sqrt{3}}\)
b) \(\sqrt{2+2\sqrt{2-\sqrt{2}}}\cdot\sqrt{2-2\sqrt{2-\sqrt{2}}}\)
c)\(\left(\sqrt{2}-\sqrt{7}\right)\sqrt{9+2\sqrt{14}}\)
