Question

Aratati ca numarul : a=2(1+2+3+...+120)-120 <<<< este patrat perfect si apoi calculati radical din a

Answer 1

            
$a=2(1+2+3+.......+120)-120 = \\ = 2( \frac{120*121}{2})-120= \\ \\ =120*121 - 120= \\ =120(121-1)= \\ =120*120= 120^{2} \,\,\,este \,\,\,patrat\,\,\,perfect \\ \\ \sqrt{120^{2}}=120$