FORMULA RADICALILOR COMPUSI:
[tex]\boxed{\sqrt{a+-\sqrt{b}}=\sqrt{\frac{a+c}{2}}+-\sqrt{\frac{a-c}{2}};unde:c=\sqrt{a^{2}-b}}[/tex]
[tex]\sqrt{3+2\sqrt{2}}-\sqrt{3-2\sqrt{2}}=?[/tex]
[tex]\sqrt{3+2\sqrt{2}}=\sqrt{3+\sqrt{8}}[/tex]
[tex]c=\sqrt{3^{2}-8}=\sqrt{9-8}=\sqrt{1}=1[/tex]
[tex]\sqrt{3+2\sqrt{2}}=\sqrt{\frac{3+1}{2}}+\sqrt{\frac{3-1}{2}}=\sqrt{\frac{4}{2}}+\sqrt{\frac{2}{2}}=\sqrt{2}+\sqrt{1}=\sqrt{2}+1[/tex]
[tex]\sqrt{3-2\sqrt{2}}=\sqrt{3-\sqrt{8}}[/tex]
[tex]c=\sqrt{3^{2}-8}=\sqrt{9-8}=\sqrt{1}=1[/tex]
[tex]\sqrt{3-2\sqrt{2}}=\sqrt{\frac{3+1}{2}}-\sqrt{\frac{3-1}{2}}=\sqrt{\frac{4}{2}}-\sqrt{\frac{2}{2}}=\sqrt{2}-1=\sqrt{2}-1[/tex]
Deci:
[tex]\sqrt{3+2\sqrt{2}}-\sqrt{3-2\sqrt{2}}=(\sqrt{2}+1)-(\sqrt{2}-1)=\sqrt{2}+1-\sqrt{2}+1=2[/tex]
