A=\(\sqrt{2}\left(3+1\right)\sqrt{2-\sqrt{3}}\)
=\(\left(\sqrt{3}+1\right)\sqrt{4-2\sqrt{3}}\)
=\(\left(\sqrt{3}+1\right)\sqrt{\left(\sqrt{3}-1\right)^2}\)
=\(\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)\)
=3-1=2
\(\sqrt{3-2\sqrt{2}}-\sqrt{11+6\sqrt{2}}\)
\(\sqrt{4-2\sqrt{3}}-\sqrt{7-4\sqrt{3}}+\sqrt{19+8\sqrt{3}}\)
\(\sqrt{6-2\sqrt{5}}+\sqrt{9+4\sqrt{5}}-\sqrt{14-6\sqrt{5}}\)
\(\sqrt{11-4\sqrt{7}}+\sqrt{23-8\sqrt{7}}+\sqrt{\left(-2^6\right)}\)
rút gọn:giải chi tiết hộ mình nha
Rút gọn các biểu thức sau:
a) \(\dfrac{2}{5}\sqrt{75}-0,5\sqrt{48}+\sqrt{300}-\dfrac{2}{3}\sqrt{12}\)
b) \(\dfrac{9-2\sqrt{3}}{3\sqrt{6}-2\sqrt{2}}+\dfrac{3}{3+\sqrt{6}}\)
c) \(3\sqrt{2}-2\sqrt{3}+2\sqrt{3}+3\sqrt{2}\)
d) \(\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}\)
e) \(\dfrac{\sqrt{a}-\sqrt{b}^2+4\sqrt{ab}}{\sqrt{a}+\sqrt{b}}-\dfrac{a\sqrt{b}-b\sqrt{a}}{\sqrt{ab}}\) với a > 0, b > 0
\(\sqrt{2+\sqrt{3}}.\sqrt{2+\sqrt{2+\sqrt{3}}}.\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}.\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}\)
\(\sqrt{2+\sqrt{2}}.\sqrt{3+\sqrt{7+\sqrt{2}}}.\sqrt{3+\sqrt{6+\sqrt{7+\sqrt{2}}}}.\sqrt{3-\sqrt{6+\sqrt{7+\sqrt{2}}}}\)
Giúp tớ với:
A=\(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
B=\(\left(\sqrt{\sqrt{6}+\sqrt{3+2\sqrt{2}}}.\sqrt{3+\sqrt{2}}.\sqrt{\sqrt{6}-\sqrt{3+2\sqrt{2}}}\right)\)
C=\(\left(\sqrt{6}-\sqrt{2}\right)\left(10+5\sqrt{3}\right)\sqrt{2-\sqrt{3}}\)
\(\frac{3+2\sqrt{3}}{\sqrt{3}}+\frac{2+\sqrt{2}}{\sqrt{2}+1}-\left(\sqrt{2}+3\right)\)
\(0.1\cdot\sqrt{\left(-3\right)^2}\cdot\left[6\sqrt{\left(\frac{1}{3}\right)^2}-\sqrt{\left(\sqrt{3}-2\right)^2}\right]^2\)
\(\left(\frac{3\sqrt{2}+\sqrt{6}}{\sqrt{12}+2}-\frac{\sqrt{54}}{3}\right)\cdot\frac{2}{\sqrt{6}}\)
\(\left(\frac{3+2\sqrt{3}}{\sqrt{3}+2}+\frac{2+\sqrt{2}}{\sqrt{2}+1}\right)\div\left(1\div\frac{1}{\sqrt{2}+\sqrt{3}}\right)\)
\(\sqrt{\frac{5+2\sqrt{6}}{5-2\sqrt{6}}}+\sqrt{\frac{5-2\sqrt{6}}{5+2\sqrt{6}}}\)
Tính
a) \(\left(\dfrac{3}{2}\sqrt{6}+2\sqrt{\dfrac{2}{3}}+4\sqrt{\dfrac{3}{2}}\right)\times\left(2\sqrt{\dfrac{2}{3}}-\sqrt{12}-\sqrt{6}\right)\)
b) \(\sqrt{6-2\sqrt{5}}-\sqrt{6+2\sqrt{5}}\)
c) \(\left(\sqrt{11+2\sqrt{24}}-\sqrt{11-2\sqrt{24}}\right):2\sqrt{3}\)
d) \(\sqrt{3-\sqrt{5}}-\sqrt{3+\sqrt{5}}\)
e) \(\sqrt{5+6\sqrt{2}}-\sqrt{9-6\sqrt{2}}-\sqrt{21-12\sqrt{3}}\)
f) \(\sqrt{6+2\sqrt{5-\sqrt{13+\sqrt{48}}}}\)
\(\frac{\sqrt{3}+\sqrt{2}-1}{2+\sqrt{6}}+\frac{\sqrt{2}-\sqrt{3}}{\sqrt{2}+1}\left(\frac{\sqrt{3}}{2-\sqrt{6}}+\frac{\sqrt{3}}{2+\sqrt{6}}\right)-\frac{1}{\sqrt{2}}\)
\(B=2+3\sqrt{2}-2\sqrt{32}-\sqrt{6+4\sqrt{2}}\)
\(G=\sqrt{12-2\sqrt{35}}+4\sqrt{20}+\sqrt{28}\)
\(E=\left(\frac{2\sqrt{2}+3\sqrt{3}}{\sqrt{2}+\sqrt{3}}-\sqrt{6}\right):\left(\sqrt{2}-\sqrt{3}\right)-\frac{2\sqrt{6}}{\sqrt{2}+\sqrt{3}}\)
1, \(\dfrac{6-\sqrt{6}}{\sqrt{6}-1}+\dfrac{6+\sqrt{6}}{\sqrt{6}}\)
2, \(\dfrac{6-6\sqrt{3}}{1-\sqrt{3}}+\dfrac{3\sqrt{3}+3}{\sqrt{3}+1}\)
3, \(\dfrac{3+\sqrt{3}}{\sqrt{3}}+\dfrac{\sqrt{6}-\sqrt{3}}{1-\sqrt{2}}\)
4, \(\dfrac{\sqrt{15}-\sqrt{12}}{\sqrt{5}-2}+\dfrac{6+2\sqrt{6}}{\sqrt{3}+\sqrt{2}}\)
5, \(\left(\dfrac{3\sqrt{125}}{15}-\dfrac{10-4\sqrt{5}}{\sqrt{5}-2}\right)\cdot\dfrac{1}{\sqrt{5}}\)
Rút gọn
a) \(\sqrt{6+3\sqrt{3}+\sqrt{6-3\sqrt{3}}}\)
b) \(\dfrac{\left(5+2\sqrt{6}\right)\left(49-20\sqrt{6}\right)\sqrt{5-2\sqrt{6}}}{9\sqrt{3}-11\sqrt{2}}\)
c) \(\sqrt{21-6\sqrt{6}}+\sqrt{9+2\sqrt{18}}-2\sqrt{6+3\sqrt{3}}\)
