Q1: How many positive integers less than 1000 have a 5th root?
Q2: How many positive integers less than 1000 have a square root and cube root?

Does anybody know an easy approach to these questions?

Please, next time create a single post for every question you pose.

regards
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Ok I will be careful new to forums.

1) We need to find the numbers with 5th root and are less than or equal to 1000. So let's say the number is x. It can be written as n^5 where n is a natural number.
So, n^5 <= 1000 gives n=1, 2, 3 as 1^5 = 5, 2^5 = 32, 3^5 = 243. But 4^5 = 1024 which is greater than 1000.

Hence the answer is 3. The numbers are 1, 32 and 243

2) We need to find the numbers with square root and cube root and are less than or equal to 1000. Again let's say the number is x.
x can be written as: ((n)^2)^3. Square of any natural number and then the cube of that number, since we have to take a cube root and a square root. So, it becomes effectively n^6 <= 1000. We can now solve it. The total number of such numbers is 3 again.
1^6 = 1
2^6 = 64
3^6 = 729

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