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The square root of 2x is greater than 3 and less than 4. How many integer values of x satisfy this condition?

 May 26, 2021
 #1
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We have 3

 May 26, 2021
 #3
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The square root of 2x is greater than 3 and less than 4. How many integer values of x satisfy this condition?  

 

3 is the square root of 9 and sqrt(2x) has to be greater than 3 so 2x has to be greater than 9.  

4 is the square root of 16 and sqrt(2x) has to be less than 4 so 2x has to be less than 16.  

 

So 2x can be 10, 11, 12, 13, 14, or 15.  But wait!  x has to be an integer, so 2x has to be even.  

 

That means 2x can be 10, 12, or 14, so x can be 5, 6, or 7

 

So the answer to "how many" is THREE.  

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 May 26, 2021

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