"Perfect" square?

Holocene

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:

[tex]\displaystyle{\sqrt{59.29} = 7.7}[/tex]

rocomath

http://en.wikipedia.org/wiki/Perfect_square

Thus a perfect square always has a square root that has no decimal expansion.

HallsofIvy

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.

dodo

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.

HallsofIvy

Quote by Dodo

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.

My calculator is under the impression that 77²= 5929, not 5229.

dodo

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

HallsofIvy

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

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Holocene	"Perfect" square? Tweet 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: [tex]\displaystyle{\sqrt{59.29} = 7.7}[/tex]

rocomath	http://en.wikipedia.org/wiki/Perfect_square Thus a perfect square always has a square root that has no decimal expansion.

HallsofIvy Recognitions: Gold Member Science Advisor 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.

dodo	"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.