Choose one number from $\{1, \ldots, 1000\}$ randomly. the probability that the chosen number is a square of an integer? a cube of an integer

Question

Choose one number from $\{1, \ldots, 1000\}$ randomly. What is the probability that the chosen number is:

a) divisible by $7$

b) a square of an integer?

c) a cube of an integer?

My answer for a is $1000/7=142$, so $142/1000$. The probability is $0.142$. But for b or c, I don't have any idea.

Answer 1

Here is my answer.

a)(1000/7)/1000=0.142

b) $31<\sqrt{1000}<32$, 31/1000=0.031.

c) $\sqrt[3]{1000}=10$, 10/1000=0.01.