Question

Полное решение со всеми действиями

Answer 1

$sqrt{13+30sqrt{2+sqrt{9+4sqrt{2}}}}=sqrt{13+30sqrt{2+sqrt{1+4sqrt{2}+8}}}=$

$1^2+4sqrt{2}+2^2sqrt{2}^2=(1+2sqrt{2})^2$

$sqrt{13+30sqrt{2+sqrt{(1+2sqrt{2})^2}}}=sqrt{13+30sqrt{1+2sqrt{2}+2}}}=sqrt{13+30sqrt{1^2+2sqrt{2}+sqrt{2}^2}}}=sqrt{13+30sqrt{(1+sqrt{2})^2}}}=sqrt{13+30(1+sqrt{2})}}}=sqrt{43+30sqrt{2}}}}=sqrt{18+30sqrt{2}+25}}}=sqrt{3^2sqrt{2}^2+2*(3sqrt{2})*5+5^2}}}=sqrt{(3sqrt{2}+5)^2}}}=3sqrt{2}+5$