Chapter 4.4, Problem 18P

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

a. Calculate the squares of 1, 2,. . ., 9 and many other whole numbers, including 17, 34, 61, 82, 99, 123, 255, 386, and 728. Record the ones digits in each case. What do you notice? Do any of your squares have a ones digit of 7, for example? Are any other digits missing from the ones digits of squares?

b. Which digits can never occur as the ones digit of a square of a whole number? Explain why some digits cannot occur as the ones digit of a square of a whole number.

c. Based on what you’ve discovered, could the number 139,787,847,234,329,483 be the square of a whole number? Why or why not?