\(=\dfrac{\sqrt{13+2\sqrt{12}}-\sqrt{13-2\sqrt{12}}+2\sqrt{12}}{\sqrt{2}}\)
\(=\dfrac{\sqrt{12}+1-\sqrt{12}+1+2\sqrt{12}}{\sqrt{2}}\)
\(=\dfrac{2\sqrt{12}+2}{\sqrt{2}}=2\sqrt{6}+\sqrt{2}\)
Tính giá trị các biểu thức:
a.\(\left(7\sqrt{48}+3\sqrt{27}-2\sqrt{12}\right)\sqrt{3}\)
b.\(\left(12\sqrt{50}-8\sqrt{200}+7\sqrt{450}\right):\sqrt{10}\)
c.\(\left(2\sqrt{6}-4\sqrt{3}+5\sqrt{2}-\dfrac{1}{4}\sqrt{8}\right)3\sqrt{6}\)
d.\(3\sqrt{15\sqrt{50}}+5\sqrt{24\sqrt{8}}-4\sqrt{12\sqrt{32}}\)
Tính thu gọn :
a , \(\sqrt{17-12\sqrt{2}}-\sqrt{17+12\sqrt{2}}\)
b , \(\sqrt{27+12\sqrt{5}}-\sqrt{27-12\sqrt{5}}\)
c , \(\sqrt{15-6\sqrt{6}}+\sqrt{15+\sqrt{6\sqrt{6}}}\)
d , \(\sqrt{4+\sqrt{15}}+\sqrt{4-\sqrt{15}}-2\sqrt{3-\sqrt{5}}\)
e , \(\sqrt{17-3\sqrt{32}}+\sqrt{17+3\sqrt{32}}\)
f , \(\sqrt{5+\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
So sánh A và B
\(A=\sqrt{12+\sqrt{12+\sqrt{12}}}+\sqrt{6+\sqrt{6+\sqrt{6+\sqrt{6}}}}\)
\(B=\sqrt{14}+\sqrt{11}\)
So sánh:
\(A=\sqrt{12+\sqrt{12+\sqrt{12}}}+\sqrt{6+\sqrt{6+\sqrt{6+\sqrt{6}}}};\\ B=\sqrt{12}+\sqrt{11}\)
Chứng minh: (\(\left(\sqrt{12}-6\sqrt{3}+\sqrt{24}\right)\sqrt{6}-\left(5\sqrt{\dfrac{1}{12}}+12\right)=-14,5\sqrt{2}\)
Rút gọn biểu thức
\(A=\sqrt{30+12\sqrt{6}}-\sqrt{21-6\sqrt{6}}\)
\(B=\sqrt{2+\sqrt{2}}.\sqrt{2+\sqrt{2+2}}.\sqrt{2-\sqrt{2+2}}\)
\(\sqrt{12-6\sqrt{3}}\)
\(\sqrt{19+8\sqrt{3}}\)
\(\sqrt{14-6\sqrt{5}}\)
tính giải chi tiết hộ mình nha
2.
a,\(\sqrt{12}-\sqrt{27}+\sqrt{3}\)
b,\(\sqrt{252}-\sqrt{700}+\sqrt{1008}-\sqrt{448};\sqrt{3}.\left(\sqrt{12}+\sqrt{27}-\sqrt{3}\right)\)
c,\(\frac{\sqrt{6}+\sqrt{10}}{\sqrt{21}+\sqrt{35}};\frac{\sqrt{405}+3\sqrt{27}}{3\sqrt{3}+\sqrt{45}}\)
d,\(\frac{\sqrt{2}+\sqrt{3}+\sqrt{4}-\sqrt{6}-\sqrt{9}-\sqrt{12}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
(\(\left(\sqrt{12}-6\sqrt{3}+\sqrt{24}\right)\cdot\sqrt{6}-\left(5\sqrt{\dfrac{1}{2}}+12\right)=-14.5\sqrt{2}\)
