The square root of 6 is an irrational number. It is also an algebraic number, a quadratic surd, an algebraic integer, a constructible number, and a computable number.
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Among other things, it belongs to the following sets: positive numbers; irrational numbers; algebraic numbers.
Rational and Real numbers
No. Negative numbers are real but their square roots are not.
Irrational: it cannot be written exactly in the decimal notation.
Integers, Rational numbers, Real numbers and Complex numbers.