Question

Помогите упростить выражение!!!!

√(4-√(15 )) + √(4+√(15 )) =
корень(4-корень (15))+корень(4+корень (15))=

Answer 1

$sqrt{4-sqrt{15}} + sqrt{4-sqrt{15}} =sqrt{10}\\\star ; ; Big ( sqrt{4-sqrt{15}}+sqrt{4+sqrt{15}} Big )^2=\\=4-underline {sqrt{15}}+2sqrt{(4-sqrt{15})(4+sqrt{15})}+4+underline {sqrt{15}}=\\=8+2sqrt{4^2-(sqrt{15})^2}=8+2sqrt{16-15}=8+2=10; ; Rightarrow \\sqrt{sqrt{4-sqrt{15}}+sqrt{4+sqrt{15}}}=sqrt{10}$