Joe is buying model rockets from a hobby store. He is buying 6 different types of rockets, tiny, small, medium, large, huge and gargantuan. All quantities of rockets bought are positive whole numbers. He buys 2 more large rockets than medium rockets. The number of small rockets he buys is equivalent to the square root of the number of large rockets he buys. The number of tiny rockets he buys is equivalent to the number of large rockets he buys plus the number of small rockets he buys plus twice the number of medium rockets he buys. The number of huge rockets he buys is equivalent to (number of medium rockets he buys + number of tiny rockets he buys + number of small rockets he buys)

^{0.5}. The number of gargantuan rockets he buys equals the number of medium rockets he buys multiplied by the number of huge rockets he buys divided by the number of small rockets he buys minus the number of large rockets he buys. Before tax, tiny rockets cost $9.75 each, small rockets cost $12.50 each, medium rockets cost $15.25 each, large rockets cost $20.00 each, huge rockets $27.20 each and gargantuan rockets cost $36.00 each. There is a sales tax of 8% on each rocket. Joe does not buy more than 300 rockets. How much does he spend on the rockets?
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