Question

 Довести, що число $sqrt{19- sqrt{3-8 sqrt{35-8 sqrt{19 } } }$ цыле

Answer 1

$sqrt{19-sqrt{3-8sqrt{35-8sqrt{19}}}}=\ sqrt{19-sqrt{3-8sqrt{(sqrt{19})^2-2*4*sqrt{19}+4^2}}}=\ sqrt{19-sqrt{3-8sqrt{(sqrt{19}-4)^2}}}=\ sqrt{19-sqrt{3-8(sqrt{19}-4)}}}=sqrt{19-sqrt{3-8sqrt{19}+32}}=\ sqrt{19-sqrt{35-8sqrt{19}}}=sqrt{19-sqrt{(sqrt{19}-4)^2}}=\ sqrt{19-sqrt{19}+4}}=sqrt{23-sqrt{19}}$