Ta có: \(12+3\sqrt{7}>12-3\sqrt{7}\Rightarrow\sqrt{12+3\sqrt{7}}>\sqrt{12-3\sqrt{7}}\Rightarrow VT>0\)
\(VT=\) bạn bình phương 2 vế lên nhé.
\(=24-2\sqrt{81}=24-18=6=VP\)
Chứng minh các bất đẳng thức sau:
\(\frac{\sqrt{\sqrt{2}+\sqrt{2}}+\sqrt{3}\sqrt{2-\sqrt{2}}}{4}< 0,8\)
(\(\sqrt{\sqrt{3}}+\sqrt{\sqrt{5}}+\sqrt{\sqrt{7}}\))-(\(\sqrt{3}+\sqrt{5}+\sqrt{7}\)) < 3
\(\sqrt{\sqrt{17+12\sqrt{2}}-\sqrt{2}}>\sqrt{3}-1\)
Rút gọn biểu thức nhiều căn
1 (\(3\sqrt{2}+\sqrt{6}\) ) . \(\sqrt{6-3\sqrt{3}}\)
2 \(\sqrt{12-3\sqrt{7}}_{ }\) - \(\sqrt{12+3\sqrt{7}}\)
\(\sqrt{7-4\sqrt{3}}\) + \(\sqrt{12+6\sqrt{3}}\)
rút gọn biểu thức trên
a,\(\left(\sqrt{27}-\sqrt{12}-\sqrt{108}-\sqrt{192}\right):\sqrt{3}\)
b,\(\frac{\sqrt{2}-\sqrt{6}}{1-\sqrt{3}}\frac{3+2\sqrt{7}}{1+\sqrt{3}}\)
c,(\(\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}\)
cho M= \(\sqrt{4+\sqrt{7}}-\sqrt{\sqrt{7}+\sqrt{3}}\) chứng minh M=\(\sqrt{2}\)
cho M=\(\dfrac{\sqrt{\sqrt{7}-\sqrt{3}}-\sqrt{\sqrt{7}+\sqrt{3}}}{\sqrt{\sqrt{7}-2}}\) chứng minh M=-\(\sqrt{2}\)
CHO M=\(\sqrt{\dfrac{3\sqrt{3}-4}{2\sqrt{3}+1}}\)+\(\sqrt{\dfrac{\sqrt{3}+4}{5-2\sqrt{3}}}\) chứng minh M=\(\sqrt{6}\)
giúp mk vs mk cần gấp lắm
a.\(\sqrt{15+6\sqrt{6}}\)
b.\(\sqrt{17-12\sqrt{2}}+\sqrt{17+12\sqrt{2}}\)
c. \(\sqrt{3-2\sqrt{2}}+\sqrt{4-2\sqrt{3}}-\sqrt{7-4\sqrt{3}}\)
\(\left(\sqrt{6}-\sqrt{5}\right)^2-\sqrt{11+2\sqrt{30}}\)
\(\sqrt{8+2\sqrt{15}}-\sqrt{8-2\sqrt{15}}\)
\(\sqrt{11+4\sqrt{7}}-\sqrt{14-6\sqrt{5}}\)
\(\sqrt{22-12\sqrt{2}}-\sqrt{19+6\sqrt{2}}\)
\(\sqrt{-6\sqrt{3}+12}+\sqrt{-12\sqrt{3}+21}\)
Tính:
a) \(\dfrac{\sqrt{7}-5}{2}-\dfrac{6-2\sqrt{7}}{4}+\dfrac{6}{\sqrt{7}-2}-\dfrac{5}{4+\sqrt{7}}\)
b) \(\dfrac{2}{\sqrt{6}-2}+\dfrac{2}{\sqrt{6}+2}+\dfrac{5}{\sqrt{6}}\)
c) \(\dfrac{1}{\sqrt{3}}+\dfrac{1}{3\sqrt{2}}+\dfrac{1}{\sqrt{3}}\sqrt{\dfrac{5}{12}-\dfrac{1}{\sqrt{6}}}\)
d) \(\dfrac{2\sqrt{3-\sqrt{3+\sqrt{13+\sqrt{48}}}}}{\sqrt{6}-\sqrt{2}}\)
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)\(\sqrt{8+2\sqrt{10+2\sqrt{5}}}+\sqrt{8-2\sqrt{10+2\sqrt{5}}}\)