# Perfect square?

1. ### Holocene

231
"Perfect" square?

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:

$$\displaystyle{\sqrt{59.29} = 7.7}$$

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4. ### HallsofIvy

40,229
Staff Emeritus
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.

Last edited: Jan 7, 2008
5. ### dodo

692
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.

6. ### HallsofIvy

40,229
Staff Emeritus
My calculator is under the impression that 772= 5929, not 5229.

7. ### dodo

692
Arrgh! Sorry, I just magnified your typo. :D

8. ### HallsofIvy

40,229
Staff Emeritus
Ooops! The original post does say "59.29", not "52.29" so you were right and I was wrong. I hate when that happens!