Irrational: it cannot be written exactly in the decimal notation.
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Among other things, it belongs to the following sets: positive numbers; irrational numbers; algebraic numbers.
Numbers that include real numbers are natural numbers, whole numbers, integers, rational numbers and irrational numbers.
Real numbers; also the rational numbers.
Of the "standard sets" -10 belongs to: ℤ⁻ (the negative integers) ℤ (the integers) ℚ⁻ (the negative rational numbers) ℚ (the rational numbers) ℝ⁻ (the negative real numbers) ℝ (the real numbers) ℂ (the complex numbers) (as ℤ ⊂ ℚ ⊂ ℝ ⊂ ℂ). Other sets are possible, eg the even numbers.
No. Negative numbers are real but their square roots are not.