Calculators are wonderful tools for approximating radicals; however, we must use caution i...

Calculators are wonderful tools for approximating radicals; however, we must use caution interpreting the results. For example, the screen in Figure A seems to indicate that  and  are exactly equal, since the eight decimal values given by the calculator agree. However, as shown in Figure B using one more decimal place in the display, they differ in the ninth decimal place. The radical expression is a very good approximation for , but it is still only an approximation.

Use your calculator to answer each question. Refer to the display for in Figure B. (Source: Eves, H., An Introduction to the History of Mathematics, © 1990 Brooks/Cole Publishing. Used with permission of Thomson Learning.)

A value for that the Greeks used circa A.D. 150 is equivalent to . In which decimal place does this value first differ from ?