✿ Salut! ✿
Pentru a rezolva exercițiul din imagine, avem nevoie de formula radicalilor compuşi.
Formula:
[tex]\sqrt{a\pm\sqrt{b}}=\sqrt{\frac{a+c}{2}}\pm\sqrt{\frac{a-c}{2}}[/tex]
[tex]c=\sqrt{a^{2}-b},\;\;\;c\in\mathbb{N}[/tex]
Exp:
[tex]a=10\\b=8\\c=\sqrt{10^{2}-8}=\sqrt{100-64}=\sqrt{36}=6[/tex]
[tex]\sqrt{10\;\boxed{+}\;\sqrt{8}}=\sqrt{\frac{10+6}{2}}\;\boxed{+}\;\sqrt{\frac{10-6}{2}}[/tex]
[tex]=\sqrt{\frac{16}{2}}+\sqrt{\frac{4}{2}}=\sqrt{8}+\sqrt{2}=2\sqrt{2}+\sqrt{2}=3\sqrt{2}[/tex]
[tex]\sqrt{10\;\boxed{-}\;\sqrt{8}}=\sqrt{\frac{10+6}{2}}\;\boxed{-}\;\sqrt{\frac{10-6}{2}}[/tex]
[tex]=\sqrt{\frac{16}{2}}-\sqrt{\frac{4}{2}}=\sqrt{8}-\sqrt{2}=2\sqrt{2}-\sqrt{2}=\sqrt{2}[/tex]
