image of colourful numbers.Can you convince me of each of the following:

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

If a square number is divided by a square number the quotient is ALWAYS a square number.

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

A number ending in 5 cannot be a perfect square unless the digit in the ten's column is a 2.

The square of any number is equal to for example:

102 = 92 + 9 + 10