Can you convince me of each of the following?

- The pattern below continues forever: $$8^2 = 7^2 + 7 + 8$$
$$9^2 = 8^2 + 8 + 9$$

- If a square number is multiplied by a square number the product is ALWAYS a square number.

- No number terminating in $2, 3, 7$ or $8$ is a perfect square.