Real Number Systems and Radicals

Identify the sets to which the following real number belongs.  Check all that apply.

Identify the sets to which the following real number belongs.  Check all that apply.

Identify the sets to which the following real number belongs.  Check all that apply.
$$-0.628$$  

Identify the sets to which the following real number belongs.  Check all that apply.

What is the following a model of?

$$\frac{\sqrt[]{5}}{\sqrt[]{10}}$$

If a non zero rational number is multiplied to an irrational number, we always get

Identify the sets to which the following real number belongs.  Check all that apply.
$$7.121221222...$$  

Identify the sets to which the following real number belongs.  Check all that apply.
$$\sqrt{100}$$  

Identify the sets to which the following real number belongs.  Check all that apply.