1. The problem statement, all variables and given/known data Determine a positive rational number whose square differs from 7 by less than 0.000001 (10^(-6)) 2. Relevant equations - 3. The attempt at a solution Let p/q be the required rational number. So, 7> (p/q)^(2) > 7-(0.000001) ⇒ √(7) > p/q > √(7-.000001) ⇒√(7) q> p > √(7-.000001)q I can't see where I'm going with this. T.T p and q are both integers, so the root quantity should be an integer for the answer Like p=q(√some perfect square that lies between 7 and 6.999999) Is this the way i am supposed to worth this out? Also how can i find such a perfect square?? Please help!! Thanks!