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How many positive integers less than 1000 have a 5th root?

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How many positive integers less than 1000 have a 5th root? [#permalink] New post 02 Dec 2017, 05:37
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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?
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Re: How many positive integers less than 1000 have a 5th root? [#permalink] New post 02 Dec 2017, 08:57
Expert's post
Please, next time create a single post for every question you pose.

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Re: How many positive integers less than 1000 have a 5th root? [#permalink] New post 02 Dec 2017, 09:47
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Carcass wrote:
Please, next time create a single post for every question you pose.

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Ok I will be careful new to forums.
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Re: How many positive integers less than 1000 have a 5th root? [#permalink] New post 11 Apr 2018, 03:01
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
Re: How many positive integers less than 1000 have a 5th root?   [#permalink] 11 Apr 2018, 03:01
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How many positive integers less than 1000 have a 5th root?

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