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4\times 3\sqrt{65}
Factor 585=3^{2}\times 65. Rewrite the square root of the product \sqrt{3^{2}\times 65} as the product of square roots \sqrt{3^{2}}\sqrt{65}. Take the square root of 3^{2}.
12\sqrt{65}
Multiply 4 and 3 to get 12.