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?

SmartMathMan
Jan 19, 2018

#1**+2 **

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

hectictar
Jan 19, 2018

#1**+2 **

Best Answer

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

hectictar
Jan 19, 2018