10. The sum of the squares of three consecutive positive integers is 770 . What is the largest of these integers?
A 15
B 16
C 17
D 18
E 19
10. C The three squares will be approximately a third of 770 , so roughly 250 . Adding up $15^{2}=225,16^{2}=256$ and $17^{2}=289$ gives the total 770 .
Alternatively, using algebra we could let $n$ be the middle integer and then add the squares $(n-1)^{2}+n^{2}+(n+1)^{2}=n^{2}-2 n+1+n^{2}+n^{2}+2 n+1=3 n^{2}+2=770$. This gives $n^{2}=256$ and hence $n=16$, so the largest integer is 17 .