+1443 Thea has a key on her calculator marked *. If an integer is displayed, pressing the * key chops off the first digit and moves it to the end. For example, if 6138 is on the screen, then pressing the * key changes the display to 1386.
Thea enters a positive integer into her calculator, then squares it, then presses the * key, then squares the result, then presses the * key again. After all these steps, the calculator displays 243. What number did Thea originally enter?
+9479 243
Do the inverse of the * function...take the last digit and move it to the front.
324
Now do the inverse of the square function.
The original number was positive, so let's take the positive square root.
18
Now do the inverse of the * function.
81
Now do the inverse of the square function.
9
+9479 243
Do the inverse of the * function...take the last digit and move it to the front.
324
Now do the inverse of the square function.
The original number was positive, so let's take the positive square root.
18
Now do the inverse of the * function.
81
Now do the inverse of the square function.
9
