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Are the square roots of all positive integers irrational? If not, give an example of the squareroot of a number that is a rational number.
No, the square roots of all positive integers are not irrational. Such as 4, 9, 16, 25, 36, ... etc. are positive integers, but their square roots are rational numbers, not an irrational number, such as:
√4 = 2 a rational number
√9 = 3 a rational number etc.