The three square numbers are 1, 9, 49.
Important information:
- Sum of three different square numbers is 59.
We need to find the square number.
Square numbers:
Square numbers less than 59 are 1, 4, 9, 16, 25, 36, 49.
Let one number be 49. Then the sum of the other two numbers must be 10 and we know that the sum of 1 and 9 is 10. So, the three numbers are 1, 9, 49.
We can check for other possibilities.
Let one number be 36. Then the sum of the other two numbers must be 23. The sum of any two square numbers cannot be equal to 23.
Let one number be 25. Then the sum of the other two numbers must be 34. The sum of 9 and 25 is 34 but we cannot include 25 two times.
Let one number be 16. Then the sum of the other two numbers must be 43. The sum of any two square numbers cannot be equal to 43.
Thus, the three square numbers are 1, 9, 49.
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