Explanation:
I am not sure what you mean. you don't round the intermediate numbers and results. only the final result.
you keep the irrational terms (like square root) like variable terms as they are and apply operations on them without actually expressing them as numbers.
only at the very last moment (when the final result is calculated) would you express them as actual number. and then you round the final result.
so, this is solved via Pythagoras :
c² = a² + b²
c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.
in our case we have
BP² = BN² + NP² = 7² + sqrt(95)² = 49 + 95 = 144
you see ?
no need ever to bring the actual result of sqrt(95) into the picture. just keep it at sqrt(95) and do with it, what you would do with any actual number.
BP² = 144
BP = sqrt(144) = 12
so, we never had to deal with the actual irrational number.
we know how it is created, so we keep using that term to represent it.