Question

Identify each number as a rationl or irrational. Explain
1.) square root of 0
2.) 1.001001001...

Answer 1

Sqrt 0 = 0 therefore rational
1.001... is irrational since you can use algebra to solve and explain

Answer 2

If you can write it down (or at least know what the next decimal is) it is rational.

you can write the square root of 0 it is 0
for 2.) it has repeating decimals so you know the next numbers or 001 001 and so on. it is rational

on the other hand, sqrt(2) is irrational because you can't write down the decimal numbers (other than one by one, after calculating it).
for example, sqrt(2)=1.41421356.... there are more decimals after the 6, but there is no pattern, the next decimal has to be figured out.