a) \(\sqrt{3-2\sqrt{2}}+\sqrt{3+2\sqrt{2}}\)
=\(\sqrt{\left(\sqrt{2}-1\right)^2}+\sqrt{\left(\sqrt{2}+1\right)^2}\)
=\(\sqrt{2}-1+\sqrt{2}+1=2\sqrt{2}\)
b) \(\sqrt{9-4\sqrt{5}}+\sqrt{6+2\sqrt{5}}\)
=\(\sqrt{\left(2-\sqrt{5}\right)^2}+\sqrt{\left(\sqrt{5}+1\right)^2}\)
= \(2-\sqrt{5}+\sqrt{5}+1=3\)
c) \(\sqrt{9-4\sqrt{2}}-\sqrt{11+6\sqrt{2}}\)
=\(\sqrt{\left(2\sqrt{2}+1\right)^2}-\sqrt{\left(3+\sqrt{2}\right)^2}\)
=\(2\sqrt{2}+1-3-\sqrt{2}=\sqrt{2}-2\)
d) \(\sqrt{12+8\sqrt{2}}+\sqrt{6-4\sqrt{2}}\)
=\(\sqrt{\left(2\sqrt{2}+2\right)^2}+\sqrt{\left(2-\sqrt{2}\right)^2}\)
=\(2\sqrt{2}+2+2-\sqrt{2}=\sqrt{2}+4\)
a)
\(\sqrt{3-2\sqrt{2}}+\sqrt{3+2\sqrt{2}}=\sqrt{2-2\sqrt{2}+1}+\sqrt{2+2\sqrt{2}+1}\\ =\sqrt{2}-1+\sqrt{2}+1=2\text{ }\sqrt{2}\)
b)
\(\sqrt{9-4\sqrt{5}}+\sqrt{6+2\sqrt{5}}=\sqrt{2^2-2.2.\sqrt{5}+5}+\sqrt{5+2\sqrt{5}+1}\\ =2-\sqrt{5}+\sqrt{5}+1=3\)
