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avatar+124 

For how many positive integers N does √N differ from 10 by less than two?

 Sep 14, 2022
 #1
avatar+9445 
+3

The difference between  √N  and  10  is less than 2. So the following two inequalities must both be true:

 

√N - 10  <  2     and      10 - √N  <  2

 

 

Looking at the first inequality:

 

√N - 10  <  2

 

√N  <  12

 

N  <  144          ( and   N > 0 )

 

 

Looking at the second inequlaity:

 

10 - √N  <  2

 

-√N  <  -8

 

√N  >  8

 

N  >  64          ( and   N > 0 )

 

 

So  N  must be a positive integer in the interval  (64, 144)

 

That is  79  integers.

 

Check

 Sep 14, 2022
 #2
avatar+124 
0

thanks its right

 Sep 14, 2022

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