3. When dividing the number $a$ by 7, we get a remainder of 3, and when dividing the number $b$ by 7, we get a remainder of 4. What is the remainder when the square of the sum of the numbers $a$ and $b$ is divided by 7? Justify your answer.
3. Write: $a=7 \cdot x+3$ ..... 1 point
Write $b=7 \cdot y+4$ ..... 1 point
$(a+b)^{2}=(7 x+7 y+7)^{2}=$ ..... 1 point
$=(7 \cdot(x+y+1))^{2}=$ ..... 1 point
$=7 \cdot\left(7 \cdot(x+y+1)^{2}\right)$ ..... 1 point
Written conclusion: The remainder is 0, since $(a+b)^{2}$ is a multiple of the number 7. ..... 1 point
Note: A solution obtained by trial and error is graded with two points.