Question

$sqrt{sqrt{8+2 sqrt{15} } - sqrt{8- \ 2 sqrt{15}} * 2+7} = ?$

Answer 1

$sqrt{left (sqrt{8+2sqrt{15}}-sqrt{8-2sqrt{15}}right )cdot 2+7}} =\\=sqrt{left (sqrt{(sqrt5+sqrt3)^2}-sqrt{(sqrt5-sqrt3)^2}right )cdot 2+7}=\\=sqrt{(|sqrt5+sqrt3|-|sqrt5-sqrt3|)cdot 2+7}=\\=sqrt{left (sqrt5+sqrt3-(sqrt5-sqrt3)right )cdot 2+7}=\\=sqrt{4sqrt3+7}=sqrt{(2+sqrt3)^2}=|2+sqrt3|=2+sqrt3$

Answer 2

Ура! Спасибо