The bases of a softball field are 60 feet apart. how far apart is home plate from second base?

So assuming that the field is a perfect square then

if you mean when you walk from home to 1st to 2nd then
60+60=120

if you mean the straight distance (as the crow flies) then
second base is diagonal from home base so

we have a right triangle with side legnths of 60 and 60

use pythagrorean theorem
a^2+b^2=c^2
a and b are legs and c=hypotonuse
60^2+60^2=c^2
3600+3600=c^2
7200=c^2
square root both sides
60 times√2=c

the distance from home base to second base=60√2