\(\sqrt{14-8\sqrt{3}}-\sqrt{24-12\sqrt{3}}=\dfrac{\sqrt{16-2.4.2\sqrt{3}+12}-\sqrt{36-2.6.2\sqrt{3}+12}}{\sqrt{2}}=\dfrac{\sqrt{\left(4-2\sqrt{3}\right)^2}-\sqrt{\left(6-2\sqrt{3}\right)^2}}{\sqrt{2}}=\dfrac{4-2\sqrt{3}-6+2\sqrt{3}}{\sqrt{2}}=\dfrac{-2}{\sqrt{2}}=-\sqrt{2}\)
thực hiện phép tính
\(\sqrt{14-8\sqrt{3}}-\sqrt{24-12\sqrt{3}}\)
Thực hiện phép tính: \(\sqrt{12}+2\sqrt{27}+3\sqrt{75}-9\sqrt{48}\)
thực hiện phép tính
\(\sqrt{2-\sqrt{3}}\left(\sqrt{5}+\sqrt{2}\right)\)
thực hiện phép tính
A=\(\sqrt{\dfrac{2-\sqrt{3}}{2+\sqrt{3}}}+\sqrt{\dfrac{2+\sqrt{3}}{2-\sqrt{3}}}\)
B=\(\sqrt{\dfrac{3-\sqrt{5}}{\sqrt{10}+\sqrt{2}}}\cdot\left(3+\sqrt{5}\right)\)
Thực hiện phép tính:
a) \(\sqrt{24+8\sqrt{5}}-\sqrt{9-4\sqrt{5}}.\)
b) \(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\).
c) \(\dfrac{1}{1+\sqrt{2}}+\dfrac{1}{\sqrt{2}+\sqrt{3}}+\dfrac{1}{\sqrt{3}+\sqrt{4}}+....+\dfrac{1}{\sqrt{99}+\sqrt{100}}.\)
Thực hiện các phép tính sau:
a)\(\dfrac{13\sqrt{12}-4\sqrt{6}}{24-4\sqrt{3}}\)
b)\(\dfrac{9\sqrt{6}-12\sqrt{3}}{3\sqrt{6}-3\sqrt{3}}\)
thực hiện phép tính
A=\(\dfrac{1}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{1}{\sqrt{2-\sqrt{2-\sqrt{3}}}}\)
B=\(\dfrac{6+4\sqrt{2}}{\sqrt{2+\sqrt{6+4\sqrt{2}}}}+\dfrac{6-4\sqrt{2}}{\sqrt{2}-\sqrt{6-4\sqrt{2}}}\)
Thực hiện phép tính:
a)\(\sqrt{12-3\sqrt{7}}-\sqrt{12+3\sqrt{7}}\)
b)\(\dfrac{\sqrt{7+\sqrt{5}}+\sqrt{7-\sqrt{5}}}{\sqrt{7+\sqrt{11}}}-\sqrt{3-2\sqrt{2}}\)
c)\(\sqrt{8+2\sqrt{10+2\sqrt{5}}}+\sqrt{8-2\sqrt{10+2\sqrt{5}}}\)
1)\(\sqrt{12}\)\(-\)\(\sqrt{27}\)\(+\)\(\sqrt{48}\)
2)(\(\sqrt{24}+\sqrt{20}-\sqrt{80}\))\(\div\)5
3)2\(\sqrt{27}-\sqrt{\dfrac{16}{3}}\)\(-\)\(\sqrt{48}-\)\(\sqrt{8\dfrac{1}{3}}\)
4) \(\dfrac{1}{\sqrt{5}-\sqrt{3}}\)\(-\)\(\dfrac{1}{\sqrt{5+\sqrt{3}}}\)
