Question

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

Answer 1

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

$1) sqrt{4+2sqrt{8+sqrt{33+8sqrt2}}}=sqrt{4+2sqrt{8+left(4sqrt2+1right)}}=\\=sqrt{4+2sqrt{left(sqrt{8}right)^2+4sqrt2+1}}=sqrt{4+2sqrt{left(2sqrt{2}right)^2+4sqrt2+1}}=\\=sqrt{4+2sqrt{left(2sqrt{2}+1right)^2}}=sqrt{4+2left|2sqrt2+1right|}=sqrt{4+2left|2sqrt2+1right|}=\\=sqrt{4+2left(2sqrt2+1right)}=sqrt{4+4sqrt2+2}=sqrt{left(2+sqrt2right)^2}=\\=left|2+sqrt2right|=2+sqrt2.$