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A perfect square is a square of an integer.The set of integers is closed under multiplication. That means that the product of any two integer is an integer. Therefore the square of an integer is an integer.
Integers are rational numbers so the square [which is an integer] is a rational number.
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Are all perfect squares rational?
Yes
Are perfect squares all rational numbers?
Yes.
Are all square roots rational numbers?
No, not all square roots are rational numbers. A rational number is a number that can be expressed as a fraction where the numerator and denominator are integers and the denominator is not zero. Square roots that are perfect squares, such as √4 or √9, are rational numbers because they can be expressed as whole numbers. However, square roots of non-perfect squares, such as √2 or √3, are irrational numbers because they cannot be expressed as a simple fraction.
What numbers always have an even number of factors?
All positive integers which are not perfect squares.
What do numbers 25 16 and 9 have in common?
The numbers 25, 16, and 9 are all perfect squares. A perfect square is a number that can be expressed as the product of an integer with itself. In this case, 25 is 5^2, 16 is 4^2, and 9 is 3^2.
