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The square root of $h$ is greater than $\dfrac{10}{3}$ and less than $\dfrac{24}{5}$. How many integer values of $h$ satisfy this condition?

 Mar 31, 2020
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10/3  <  √h  < 24/5

 

So  we  have this  10/3 < √h      square both sides

100/9 < h

And

√h < 24/5     square both sides

h  = 576/25

 

So  we  have  that

 

100/9  < h  < 576/25

Note  that 100/9 =  11+ 1/9

So

11 + 1/9 < h

 

And  576/25  = 23  +  1/25

So  h < 2

 

So the number of  integers that  satisfy  this  =    23 - 12  + 1  =  12

 

 

cool cool cool

 Mar 31, 2020

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