The discussion clarifies that a perfect square is defined as the square of an integer, which results in a whole number without a decimal expansion. The example provided, \(\sqrt{59.29} = 7.7\), illustrates that while 59.29 has a decimal root, it is not classified as a perfect square. The conversation also highlights that 5229 is a perfect square, as it can be expressed as \((77/10)^2\), demonstrating the relationship between rational numbers and perfect squares.
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My calculator is under the impression that 772= 5929, not 5229.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.