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

helpppp Apr 3, 2020

#1**+1 **

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.

!

asinus Apr 3, 2020

#2**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!

MooMooooMooM Apr 3, 2020