Given: √(29 − 12√5) = a + b√n  

Step 1: Square both sides  
(a + b√n)^2 = 29 − 12√5  
a^2 + n b^2 + 2ab√n = 29 − 12√5  

Step 2: Equate rational and irrational parts  
Rational part: a^2 + n b^2 = 29  
Irrational part: 2ab√n = −12√5  
=> ab√n = −6√5  
=> n = 5, ab = −6  

Step 3: Solve a^2 + 5b^2 = 29 with ab = −6  
Possible values: (a = 3, b = −2) or (a = −3, b = 2)  

Step 4: Identify positive and negative roots  
Positive root: −3 + 2√5  
Negative root: 3 − 2√5  

Step 5: To maximize a + b + n, modify the expression:  
Take a = −3, b = 1, n = 20  

Step 6: Compute maximum possible value  
a + b + n = −3 + 1 + 20 = 18  

Answer: Maximum possible value of (a + b + n) = 18