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For how many positive integers $N$ does $\(\sqrt{N}\)$ differ from 10 by less than 2?

 Apr 3, 2020
 #1
avatar+9457 
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For how many positive integers N does \(\sqrt{N}\)  differ from 10 by less than 2?

 

Hello helpppp!

 

Für wie viele positive ganze Zahlen N  unterscheidet sich \(\sqrt{N}\) von 10 um weniger als 2?

 

\(0\le (10-\sqrt{N})<2\\ 10\ge\sqrt{N}>8\\ \color{blue}N\in\{65...100\}\)

 

For 36 positive integers N does \(\sqrt{N}\) differ  from 10 by less than 2.

laugh  !

 Apr 3, 2020
edited by asinus  Apr 3, 2020
 #2
avatar+252 
0

I got a different answer, asinus-

sqrtN has to be greater than 8 and less than 12 - which is greater than \(\sqrt{64}\) and less than \(\sqrt{144}\). That means N can be anywhere between 65 and 143. Subtract 64 from both sides to get that N can be from 1 - 79, which is 79 integers. I think by 'differ' you interperted it as sqrtN has to be smaller than 10...

 

Please notify me if I am wrong in how I interpreted it!

 

coolsmileycool

 Apr 3, 2020

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