Chapter 4.4, Problem 17P

* The square of a number is just the number times itself. For example, the square of 4 is $4.4=16.$

a. Find the squares of the numbers 15, 25, 35, 45, ..., 95, 105, 115, 125, ..., 195, 205, and three other whole numbers that end in 5.

b. Find some patterns in the answers to part (a).

Specifically, in all of your answers to part (a), what do you notice about the last two digits, and what do you notice about the number formed by deleting the last two digits?

c. Use what you discovered in part (b) to predict the squares of 2,005 and 10,005.

d. Every whole number ending in 5 must be of the form $10A+5$ for some whole number A. Find the square of $10A+5$ —namely, calculate $10A+5$ . $10A+5$ .

e. How does your answer to part (d) explain the pattern you found in part (b)?