\(\left(\sqrt{3}-\sqrt{2}\right)\sqrt{5+2\sqrt{6}}\)
\(=\sqrt{15+2.3.\sqrt{6}}\)\(-\sqrt{10+2.2\sqrt{6}}\)
\(=\sqrt{9+2.3\sqrt{6}+6}\)\(-\sqrt{6+2.\sqrt{6}.2+4}\)
\(=\sqrt{\left(3+\sqrt{6}\right)^2}\)\(-\sqrt{\left(\sqrt{6}+2\right)^2}\)
\(=3+\sqrt{6}\)\(-2\)\(-\sqrt{6}=\left(3-2\right)+\left(\sqrt{6}-\sqrt{6}\right)\)
\(=1+0=1\)
a) \((\sqrt{3}-\sqrt{2}).\sqrt{(\sqrt{3}+\sqrt{2})^2}\)
\(\left(\sqrt{3}-\sqrt{2}\right).\left(\sqrt{3}+\sqrt{2}\right)\)
\(\left(\sqrt{3}\right)^2-\left(\sqrt{2}\right)^2\)\(=3-2=1\)
b) \(\sqrt{24+8\sqrt{5}}+\sqrt{9-4\sqrt{5}}\)
=\(\sqrt{(2+2\sqrt{5})^2}+\sqrt{(\sqrt{5}-2)^2}\)
=\(2+2\sqrt{5}+\sqrt{5}-2\)\(=3\sqrt{5}\)
a)=\(1\)
b)\(3\sqrt{5}\)
\(a,\left(\sqrt{3}-\sqrt{2}\right)\sqrt{5+2\sqrt{6}}\\ =\left(\sqrt{3}-\sqrt{2}\right).\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}\\ =\left(\sqrt{3}-\sqrt{2}\right).\left(\sqrt{3}+\sqrt{2}\right)\\ =\left(\sqrt{3}\right)^2-\left(\sqrt{2}\right)^2\\ =3-2\\ =1\\ b,\sqrt{24+8\sqrt{5}+\sqrt{9-4\sqrt{5}}}\\ =\sqrt{\left(2+2\sqrt{5}\right)^2+\sqrt{\left(\sqrt{5-2}\right)^2}}\\ =2+2\sqrt{5}-\sqrt{5}-2\\ =3\sqrt{5}\)
a) = 1
b) = \(3\sqrt{5}\)
a) = 1
b) \(3\sqrt{5}\)
a\()\)\((\sqrt{3}-\sqrt{2})\sqrt{5+2\sqrt{6}}\)
=\(\sqrt{3}-\sqrt{2}).\sqrt{(\sqrt{3}+\sqrt{2})^2}\)
=\((\sqrt{3}-\sqrt{2}).\sqrt{3}+\sqrt{2)}\)
=\((\sqrt{3})^2-(\sqrt{2})^2=3-2=1\)
b\()\)\(\sqrt{24+8\sqrt{5}}+\sqrt{9-4\sqrt{5}}\)
=\(\sqrt{(2+2\sqrt{5)^2}}+\sqrt{(\sqrt{5-2)^2}}\)
=2+2\(\sqrt{5}+\sqrt{5}-2\)
=3\(\sqrt{5}\)
a) = 1 b) = \(3\sqrt{5}\)
\(a.\left(\sqrt{3}-\sqrt{2}\right)\sqrt{5+2\sqrt{6}}\)
\(=\left(\sqrt{3}-\sqrt{2}\right).\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}\)
\(=\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)\)
\(=\left(\sqrt{3}\right)^2-\left(\sqrt{2}\right)^2\)
\(=3-2=1\)
\(b.\sqrt{24+8\sqrt{5}}+\sqrt{9-4\sqrt{5}}\)
\(=\sqrt{\left(2+2\sqrt{5}\right)^2}+\sqrt{\left(\sqrt{5}-2\right)^2}\)
\(=2+2\sqrt{5}+\sqrt{5}-2\)
\(=3\sqrt{5}\)
a) =1
b) =\(3\sqrt{5}\)
a, \(\left(\sqrt{3}-\sqrt{2}\right)\sqrt{5+2\sqrt{6}}\)
= \(\left(\sqrt{3}-\sqrt{2}\right)\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}\)
= \(\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)\)
= \(\left(\sqrt{3}\right)^2-\left(\sqrt{2}\right)^2\)
= \(3-2\)= \(1\)
b, \(\sqrt{24+8\sqrt{5}}+\sqrt{9-4\sqrt{5}}\)
= \(\sqrt{\left(2+2\sqrt{5}\right)^2}+\sqrt{\left(\sqrt{5}-2\right)^2}\)
= \(2+2\sqrt{5}+\sqrt{5}-2\)
= \(3\sqrt{5}\)
a) 1
b) 3\(\sqrt{5}\)
a) \(\left(\sqrt{3}-\sqrt{2}\right)\sqrt{5+2\sqrt{6}}\)
=\(\left(\sqrt{3}-\sqrt{2}\right)\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}\)
=3 - 2
= 1
b)\(\sqrt{24+8\sqrt{5}}+\sqrt{9-4\sqrt{5}}\)
=\(\sqrt{20+8\sqrt{5}+4}+\sqrt{5-4\sqrt{5}+4}\)
=\(\sqrt{\left(2\sqrt{5}+2\right)^2}+\sqrt{\left(\sqrt{5}-2\right)^2}\)
=\(2\sqrt{5}+2+\sqrt{5}-2\)
= \(3\sqrt{5}\)
a) = 1
b) = 3\(\sqrt{5}\)
a) 1
b) \(3\sqrt{5}\)
a)1
b)\(3\sqrt{5}\)
a) 1
b) 3\(\sqrt{5}\)
a) 1
b) 3 căn 5
a) 1
b) \(3\sqrt{5}\)
a) 1
b) 3\(\sqrt{5}\)
a) 1
b) \(3\sqrt{5}\)
a) 1
b) 3\(\sqrt{5}\)
a) 1
b) 3\(\sqrt{5}\)
a)1
b)3\(\sqrt{5}\)
a) 1
b) 3\(\sqrt{5}\)