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A principal square root is any square root that's answer is positive, and a perfect square root is a square root that's answer is an integer.

Q: What is the difference between principal square root and perfect square root?

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None, although "perfect square" tends to be used for whole numbers.

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 smallest perfect squares that end with 9 are 9 (the square of 3) 49 (the square of 7). Their difference is 40.

The square root of a perfect square is a whole number. Example sqrt(36) = 6 so 36 is a perfect square Example sqrt(25) = 5 so 25 is a perfect square Example sqrt(8)= 2.828 which is not whole so 8 is not a perfect square

Perfect square roots are square roots that have a whole number that can go into it perfectly. Nonperfect square roots are square roots that have decimal numbers going into it. Example: Perfect Square Root: 144- Square Root: 12 Nonperfect Square Root: 24- Square Root: About 4.89

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No, but a perfect square is usually the square of a whole number.

None, although "perfect square" tends to be used for whole numbers.

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 smallest perfect squares that end with 9 are 9 (the square of 3) 49 (the square of 7). Their difference is 40.

The square root of a perfect square is a whole number. Example sqrt(36) = 6 so 36 is a perfect square Example sqrt(25) = 5 so 25 is a perfect square Example sqrt(8)= 2.828 which is not whole so 8 is not a perfect square

There is not a number that is a perfect square and perfect cube between 1 and 25.There is not a number that is a perfect square and perfect cube between 1 and 25.There is not a number that is a perfect square and perfect cube between 1 and 25.There is not a number that is a perfect square and perfect cube between 1 and 25.

Perfect square roots are square roots that have a whole number that can go into it perfectly. Nonperfect square roots are square roots that have decimal numbers going into it. Example: Perfect Square Root: 144- Square Root: 12 Nonperfect Square Root: 24- Square Root: About 4.89

"Perfect square" means that you square a whole number. Sometimes simply called "square" or "square number". "Difference of two squares" is the result of subtracting one such square from another. In most cases, the difference will not itself be a square.

the square root of 1280 is between 35.7 and 35.8 therefore it is NOT a perfect square.

Since a thousand squared is a million, the "smallest..." is the square of 1001, and the "largest..." is the square of 999.

The square root of a non-perfect square may be irrational and therefore may not be easy to find. However, it need not be.For example, 2.25 is not a perfect square but 2.25 = 9/4 and both 9 and 4 are perfect squares. So sqrt(2.25) = sqrt(9/4) = sqrt(9)/sqrt(4) = 3/2 = 1.5. Not that difficult!

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