Question

Полное решение со всеми действиями

Answer 1

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

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

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