How can I Find the size of each of the following sets

Question

I got this question for homework and can't solve it please help

Find the size of the following sets

1.{x|x∈Z and x^2=8}.

2.P(A), where A=P({1,2}).

3.{1,10,100,1000,…}.

4.S×T, where S={a,b,c} and T={1,2,3,4,5}.

5.{x|x∈Z and x^2<8}.

Answer 1

1. Solve the equation for x.
2. Calculate P(A) and count the sets.
3. That set = { 10$^n$ : n nonnegative integer }.
4. Prove |A×B| = |A|×|B|.
5. One by one find the integers with square < 2.
   How far will you have to look?