c)
\(\sqrt{\left(\sqrt{2}-3\right)^2}-\sqrt{3+2\sqrt{2}}\\ =\left|\sqrt{2}-3\right|-\sqrt{2+2\sqrt{2}+1}\)
\(=3-\sqrt{2}-\sqrt{\left(\sqrt{2}+1\right)^2}\) (\(\sqrt{2}-3< 0\))
\(=3-\sqrt{2}-\left|\sqrt{2}+1\right|\)
\(=3-\sqrt{2}-\left(\sqrt{2}+1\right)\) (vì \(\sqrt{2}+1>0\))
\(=3-\sqrt{2}-\sqrt{2}-1\\ =2-2\sqrt{2}\)
1. Thu gọn
a) A=\(\left(\sqrt{3+2\sqrt{2}}-\sqrt{3-2\sqrt{2}}\right)\left(\sqrt{3-2\sqrt{2}}+\sqrt{3+2\sqrt{2}}\right)\)
b) B=\(\sqrt{2+\sqrt{3}}.\sqrt{2+\sqrt{2+\sqrt{3}}}.\sqrt{2-\sqrt{2-\sqrt{3}}}\)
c) C=\(\dfrac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
Thực hiện các phép tính
a) \(\sqrt{2+\sqrt{3}}.\sqrt{2+\sqrt{2+\sqrt{3}}}.\sqrt{2-\sqrt{2+\sqrt{3}}}\)
b) \(\left(\sqrt{6}+\sqrt{2}\right).\left(\sqrt{3}-2\right)\sqrt{\sqrt{3+2}}\)
c) \(\sqrt{12-3\sqrt{7}}-\sqrt{12+3\sqrt{7}}\)
a) \(\sqrt{5+2\sqrt{6}}-\sqrt{3-2\sqrt{2}}\)
b) \(\sqrt{11+6\sqrt{2}}-\sqrt{18+8\sqrt{2}}\)
c) \(\sqrt{2}\sqrt{2-\sqrt{3}}\left(\sqrt{3}+1\right)\)
Bài 1 :Chứng minh các đẳng thức :
a ) \(2\sqrt{2}\left(\sqrt{3}-2\right)\) + \(\left(1+2\sqrt{2}\right)^2-2\sqrt{6}=9\)
b ) \(\sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}}=\sqrt{6}\)
c ) \(\sqrt{11-6\sqrt{2}}+\sqrt{11+6\sqrt{2}}=6\)
Bài 2 : Rút gọn các biểu thức sau :
a ) \(\frac{1}{\sqrt{5}+\sqrt{3}}-\frac{1}{\sqrt{5}-\sqrt{3}}\)
b ) \(\frac{\sqrt{4-2\sqrt{3}}}{\sqrt{6}-\sqrt{2}}\)
c ) \(\frac{1}{2+\sqrt{3}}+\frac{\sqrt{2}}{\sqrt{6}}-\frac{2}{3+\sqrt{3}}\)
Bài 3 : Rút gọn các biểu thức sau :
a ) \(\sqrt{20}-\sqrt{45}+3\sqrt{18}+\sqrt{72}\)
b ) \(\left(\sqrt{28}-2\sqrt{3}+\sqrt{7}\right)\sqrt{7}+\sqrt{84}\)
c ) \(\left(\sqrt{6}+\sqrt{5}\right)^2-\sqrt{120}\)
d ) \(\left(\frac{1}{2}\sqrt{\frac{1}{2}}-\frac{3}{2}\sqrt{2}+\frac{4}{5}\sqrt{200}\right):\frac{1}{8}\)
bài 5 Tính:
a) \(\sqrt{6-2\sqrt{5}}\)
b)\(\sqrt{7-4\sqrt{3}}\)
c)\(\sqrt{3-2\sqrt{2}}\) -\(\sqrt{6-4\sqrt{2}}\)
d)\(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)
Rút gọn biểu thức
a)A=\(\sqrt{3-2\sqrt{2}}\)
b)B=\(\sqrt{3-2\sqrt{2}}-\sqrt{6+4\sqrt{2}}\)
c)C=\(\sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}}\)
c,\(\sqrt{(2\sqrt{2}-3)^2}-\sqrt{3+2\sqrt{2}}\)
tính:
a,\(\sqrt{9-4\sqrt{5}}-\sqrt{5}\)
b,\(\sqrt{7-4\sqrt{3}}+\sqrt{4-2\sqrt{3}}\)
c,\(\dfrac{x-49}{\sqrt{x}-7}\)
d,\(\sqrt{4+2\sqrt{3}}-\sqrt{13+4\sqrt{3}}\)
e,\(2+\sqrt{17-4\sqrt{9+4\sqrt{45}}}\)
Tính:
a, A = \(\sqrt{3+2\sqrt{2}}-\sqrt{6-4\sqrt{2}}\)
b, B = \(\sqrt{6-2\sqrt{5}+\sqrt{6+2\sqrt{5}}}\)
c, C = \(\sqrt{1+2\sqrt{1+2\sqrt{3+2\sqrt{2}}}}\)
d, D = \(\sqrt{6+2\sqrt{5-\sqrt{13+4\sqrt{3}}}}\)
e, E = \(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)
