Question

Докажите тождество !Решите первый и второй пример !Алгебра 8 класс корни! Даю 20 баллов!!!!!!!!!!!!!!!!!11

Answer 1

$2)\ \sqrt{33+8\sqrt2}=\sqrt{32+8\sqrt2+1}=\sqrt{\left(\sqrt{32}\right)^2+8\sqrt2+1}=\\\\=\sqrt{\left(\sqrt{4^2\cdot2}\right)^2+8\sqrt2+1}=\sqrt{\left(4\sqrt{2}\right)^2+8\sqrt2+1}=\\\\=\sqrt{\left(4\sqrt2+1\right)^2}=\left|4\sqrt2+1\right|=4\sqrt2+1;$

$1)\ \sqrt{4+2\sqrt{8+\sqrt{33+8\sqrt2}}}=\sqrt{4+2\sqrt{8+\left(4\sqrt2+1\right)}}=\\\\=\sqrt{4+2\sqrt{\left(\sqrt{8}\right)^2+4\sqrt2+1}}=\sqrt{4+2\sqrt{\left(2\sqrt{2}\right)^2+4\sqrt2+1}}=\\\\=\sqrt{4+2\sqrt{\left(2\sqrt{2}+1\right)^2}}=\sqrt{4+2\left|2\sqrt2+1\right|}=\sqrt{4+2\left|2\sqrt2+1\right|}=\\\\=\sqrt{4+2\left(2\sqrt2+1\right)}=\sqrt{4+4\sqrt2+2}=\sqrt{\left(2+\sqrt2\right)^2}=\\\\=\left|2+\sqrt2\right|=2+\sqrt2.$