Question 1104299
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The prime factorization of 3600 is (2^4)(3^2)(5^2).<br>
If 3600 = ab^2c^3, then c must be 2, because 2 is the only prime factor that occurs 3 or more times.<br>
That means ab^2 = 2(3^2)(5^2).<br>
There are only two possibilities:
(1) b^2=3^2 and a = 2(5^2) = 50; that makes a+b+c = 50+3+2 = 55; or
(2) b^2=5^2 and a = 2(3^2) = 18; that makes a+b+c = 18+5+2 = 25.<br>
The minimum value of a+b+c is 25.