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There is a partial relationship. The principal square root of a perfect square is the number itself. For example, the principal square root of 5^2 = the principal square root of 25 = the positive element in {-5, 5} = 5. The converse is not true. The number 3, for example, has a square root which are approx -1.7321 and 1.7321. But the square of either of these numbers is 3, but that is not a perfect square since it is not the square of an integer.
The square root of a positive number results in a positive number. For example, the square root of 25 is 5. * * * * * Not true! There are two real square roots for every positive number: one positive and one negative. -5 is as much a square root of 25 as +5 is. However, the positive root is the principal root and so is often presented as the only root.
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