Question

aratati ca 9ori(5+10+15+.....+200):4 este patrat perfect.

Answer 1

9·(5+10+15+...+200):41=          pp= ?
9.5·(1+ 2+ 3+...+40):41=
45·40·41:2:41=
45·20=
2²·3²·5²= pp
30²

Answer 2

$\displaystyle 9 \cdot (5+10+15+...+200):41=9 \cdot 5(1+2+3+...+40):41= \\ \\ =45(1+2+3+...+40):41=45 \cdot \frac{40(40+1)}{2}:41 = \\ \\ =45 \cdot \frac{40 \cdot 41}{2}:41 =45 \cdot \frac{1640}{2} :41=45 \cdot 820:41=45 \cdot 20=900=30^2$