Question

Решите двойной радикал

Answer 1

$a=sqrt{21+2sqrt{38}}+sqrt{21-sqrt{38}}=$

$=sqrt{19+2sqrt{19*2}+2}+sqrt{19-2sqrt{19*2}+2}= \ \ =sqrt{(sqrt{19}+sqrt{2})^2}+sqrt{(sqrt{19}-sqrt{2})^2}= \ \ =|sqrt{19}+sqrt{2}|+|sqrt{19}-sqrt{2}|=$

$=sqrt{19}+sqrt{2}+sqrt{19}-sqrt{2}=2sqrt{19}$