+0

# non integer square roots

-5
166
2
+-280

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

Apr 3, 2020

#1
+10573
+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.

!

Apr 3, 2020
edited by asinus  Apr 3, 2020
#2
+262
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!

Apr 3, 2020