Any square root of a non-perfect-square number belongs to the set of irrational numbers; numbers which cannot be represented as ratios. Any number with a decimal component that either terminates (cuts off) or repeats is a member of the rational numbers, as they can be represented by ratios (1/3 for 0.3333... and 743/100 7.43). Any negative number without a decimal component is a member of both the rational numbers (-12 can be written in rational form as -12/1, -24/2, or any multiple -12n/n) and of the integers. Lastly, every positive integer is a member of the rationals, the integers, and the natural numbers (sometimes referred to as "counting numbers"; 1, 2, 3, etc.).
Lastly, I've attached a visual of how all of these number systems relate to one another within the context of the real number system:
