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How many positive whole numbers have cube roots that are less than 10 but greater than 5?

 Apr 4, 2021
 #1
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How many positive whole numbers have cube roots that are less than 10 but greater than 5?     

 

Maybe I'm missing something, but it would seem to me that the number of cubes that satisfy the conditions would be the same as the number of cube roots that satisfy the conditions.  The number of whole cube roots 10 > x > 5 is four, namely 6, 7, 8, and 9.  If I'm correct, then the answer to the problem is those four.

 Apr 4, 2021
 #2
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I've reconsidered the question.  Here's my new take on it.  

 

You want the whole numbers whose cube roots are 10 < x < 5. 

 

The problem did not say that the roots have to be whole numbers. 

 

103 is 1,000 and 53 is 125.  You want every whole number 1,000 < x < 125,   

 

You want all the numbers from 999 to 126 inclusive.  How many is that.  874  

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 Apr 4, 2021

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