Can you guess their ages?

Logic Level 4

One day, Mr. Alfred, the mathematician, was returning home when suddenly he met Dr. Bertrand, the scientist. Dr. Bertrand asked: "Oh Alfred! Good to see you after such a long time. How old are your three sons now?" Mr. Alfred said: "The product of their ages is 36." Dr. Bertrand asked: "Yes but what are their ages?" Mr. Alfred said: "Well, Bertrand, their ages add up to your house number." Dr. Bertrand asked: "That's fine but their ages..?" Mr. Alfred said: "You see, Bertrand, my eldest son has already started taking lessons on trigonometry and he understands the subject quite well." Dr. Bertrand exclaimed: "Ah! Now I know their ages." Well, Dr. Bertrand was quite aware of his own house number. But you are not, right? So, without knowing his house number, can you too find their ages? If you can, then write down the sum of squares of their ages. (Assume that Dr. Bertrand is a genius with super-fast mental computational abilities and that the ages of the sons are integer years.)

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