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No, it is neither rational nor irrational. It is a complex number.

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Q: Is the square root of negative 1 irrational?
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Is the square root of x and the square root of NEGATIVE x both rational and irrational?

Yes, because when x equals 1, the square root of x is rational and the square root of -x is irrational, and when x equals -1, the square root of x is irrational and the square root of -x is rational.


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The sum, or difference, of two irrational numbers can be rational, or irrational. For example, if A = square root of 2 and B = square root of 3, both the sum and difference are irrational. If A = (1 + square root of 2), and B = square root of 2, then, while both are irrational, the difference (equal to 1) is rational.


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