Question

# If ( (A B)^{2}=C C B ) (A,B, ( C ) are unequal and ( A, C eq 0 ) ) where ( A B ) is a two digit number and ( operatorname{CCB} ) is a three digit number, then find the minimum value of ( A+B+C )

Solution

from observation we can say that

( A B=15 )

((AB) = 225 = CCB)

(A =1 B = 5, C = 2)

(= min A + B + C = 8)