Odpowiedź:
[tex]a)\ \ \sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{4}}}}}}=\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+2}}}}}=\\\\\\=\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{4}}}}}=\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+2}}}}=\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{4}}}}=\\\\\\=\sqrt{2+\sqrt{2+\sqrt{2+2}}}=\sqrt{2+\sqrt{2+\sqrt{4}}}=\sqrt{2+\sqrt{2+2}}=\sqrt{2+\sqrt{4}}=\sqrt{2+2}=\\\\=\sqrt{4}=2[/tex]
[tex]b)\ \ \sqrt{3\cdot\sqrt{3\cdot\sqrt{3\cdot\sqrt{3\cdot\sqrt{3\cdot\sqrt{9}}}}}}=\sqrt{3\cdot\sqrt{3\cdot\sqrt{3\cdot\sqrt{3\cdot\sqrt{3\cdot3}}}}}=\\\\\\=\sqrt{3\cdot\sqrt{3\cdot\sqrt{3\cdot\sqrt{3\cdot\sqrt{9}}}}}=\sqrt{3\cdot\sqrt{3\cdot\sqrt{3\cdot\sqrt{3\cdot3}}}}=\sqrt{3\cdot\sqrt{3\cdot\sqrt{3\cdot\sqrt{9}}}}=\\\\\\=\sqrt{3\cdot\sqrt{3\cdot\sqrt{3\cdot3}}}=\sqrt{3\cdot\sqrt{3\cdot\sqrt{9}}}=\sqrt{3\cdot\sqrt{3\cdot3}}=\sqrt{3\cdot\sqrt{9}}=\sqrt{3\cdot3}=\\\\=\sqrt{9}=3[/tex]
