# "Perfect" square?

by Holocene
Tags: perfect, square
 P: 231 Is a perfect square only "perfect" if the root is a whole number? Or does the term just dictate that decimals must eventually terminate? For instance: $$\displaystyle{\sqrt{59.29} = 7.7}$$
 P: 1,757 http://en.wikipedia.org/wiki/Perfect_square Thus a perfect square always has a square root that has no decimal expansion.
 Math Emeritus Sci Advisor Thanks PF Gold P: 38,882 A number always has a "decimal expansion". Integers just happen to have all 0s after the decimal point! A "perfect square" is the square of an integer. 52.29 is NOT a perfect square.
P: 688

## "Perfect" square?

Though 5229 is a perfect square. If you have a rational number as the result of a root, then the thing inside the root is the square of a rational (in this case, (77/10)^2 = 5229/100), so there are two perfect squares involved somewhere. Other than these musings, all the replies above are, of course, right.
Math
Emeritus