Is \sqrt{59.29} a perfect square?Perfect Square: Whole vs Decimals

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Discussion Overview

The discussion centers around the concept of perfect squares, specifically whether the term applies only to whole numbers or if it can include decimal values. Participants explore the implications of square roots of decimal numbers and the definitions surrounding perfect squares.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants question whether a perfect square must have a whole number as its square root or if decimals can also be considered, suggesting that decimals might need to terminate.
  • One participant asserts that a perfect square is defined as the square of an integer, implying that numbers like 59.29 are not perfect squares.
  • Another participant introduces the idea that if a square root results in a rational number, then the number under the root could be the square of a rational number, leading to a discussion about the nature of perfect squares in this context.
  • There is a correction regarding a typo in the numbers discussed, with participants acknowledging the mix-up between 59.29 and 52.29.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the definition of perfect squares, with multiple competing views on whether decimals can be included and what constitutes a perfect square.

Contextual Notes

There are unresolved assumptions regarding the definitions of perfect squares and the implications of rational versus integer roots. The discussion also highlights the potential for confusion in numerical representation.

Holocene
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"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:

[tex]\displaystyle{\sqrt{59.29} = 7.7}[/tex]
 
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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.
 
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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.
 
Dodo said:
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.
 
Arrgh! Sorry, I just magnified your typo. :D
 
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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