Thực hiện các phép tính sau:
a, \(\left(\sqrt{6}+\sqrt{2}\right)\cdot\left(\sqrt{3}-2\right)\cdot\sqrt{\sqrt{3}+2}\)
b, \(\left(4+\sqrt{15}\right)\cdot\left(\sqrt{10}-\sqrt{6}\right)\cdot\sqrt{4-\sqrt{15}}\)
c, \(\sqrt{13-\sqrt{160}}-\sqrt{53+4\sqrt{90}}\)
d, \(\sqrt{6-2\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-\sqrt{128}}}}\)
Thực hiện các phép tính sau:
a, \(\sqrt{2+\sqrt{3}}-\sqrt{2-\sqrt{3}}\)
b, \(\sqrt{21-12\sqrt{3}}-\sqrt{3}\)
c, \(\left(\sqrt{6}+\sqrt{2}\right)\cdot\left(\sqrt{3}-2\right)\sqrt{\sqrt{3}+2}\)
d, \(\left(4+\sqrt{15}\right)\cdot\left(\sqrt{10}-\sqrt{6}\right)\cdot\sqrt{4-\sqrt{15}}\)
e, \(\sqrt{13-\sqrt{160}}-\sqrt{53+4\sqrt{90}}\)\
f, \(\sqrt{6-2\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18}-\sqrt{128}}}\)
thực hiện phép tính
a)\(\left(2\sqrt{6}-4\sqrt{3}+5\sqrt{2}-\frac{1}{4}\sqrt{8}\right)\cdot3\sqrt{6}\)
b)\(2\sqrt{2}\left(2-3\sqrt{3}\right)+\left(1-2\sqrt{2}\right)^2+6\sqrt{6}\)
c)\(\left(20\sqrt{300}-15\sqrt{675}+5\sqrt{75}\right):\sqrt{15}\)
Thực hiện phép tính ( rút gọn biểu thức )
a) \(\left(\sqrt{14}+\sqrt{6}\right)\sqrt{5-\sqrt{21}}\)
b) \(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\)\(\sqrt{4-\sqrt{15}}\)
Thực hiện phép tính:
a)\(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
b)\(\sqrt{3+\sqrt{5}}-\sqrt{3-\sqrt{5}}-\sqrt{2}\)
Thực hiện phép tính và thu gọn biểu thức:
B= \(\left(\dfrac{4}{1-\sqrt{5}}+\dfrac{1}{2+\sqrt{5}}-\dfrac{4}{3-\sqrt{5}}\right)\left(\sqrt{5}-6\right)\)
Thực hiện phép tính:
\(\sqrt{48}-\dfrac{\sqrt{21}-\sqrt{15}}{\sqrt{7}-\sqrt{5}}+\dfrac{2}{\sqrt{3}+1}\)
a)\(\sqrt{\left(2\sqrt{2}-3\right)^2+\sqrt{15}}\)
b)\(\sqrt{\left(\sqrt{10}-3\right)}^2+\sqrt{\left(\sqrt{10}-4\right)^2}\)
c)\(11+6\sqrt{2}=\left(3+\sqrt{2}\right)^2\)
d)\(\sqrt{11}+6\sqrt{2}+\sqrt{11-6\sqrt{2}=6}\)
Tính
A= \(\sqrt{\left(1-\sqrt{3}\right)^2}-\sqrt{\left(\sqrt{3}+2\right)^2}\)
B=\(\sqrt{\left(2-\sqrt{3}\right)^2}+\sqrt{4-2\sqrt{3}}\)
C=\(\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}\)
Thực hiện phép tính
a) \(\left(2-\sqrt{3}\right)^2-\sqrt{4-2\sqrt{3}}+\sqrt{12}\)
b)\(\frac{2\sqrt{12}-\sqrt{6}}{2\sqrt{6}-\sqrt{3}}+\frac{10+\sqrt{5}}{2\sqrt{15}+\sqrt{3}}\)
c)\(\left(\frac{3+2\sqrt{3}}{\sqrt{3}+2}+\frac{2+\sqrt{2}}{\sqrt{2}+1}\right):\left(\sqrt{2}+\sqrt{3}\right)\)
d)\(\sqrt{10-4\sqrt{6}}+\sqrt{33-12\sqrt{6}}\)
e)\(\sqrt{16-6\sqrt{7}}+\sqrt{32-8\sqrt{7}}\)
f)\(\sqrt{28-16\sqrt{3}}+\sqrt{73-40\sqrt{3}}\)