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6\times 20\sqrt{12756598641331885}
Factor 5102639456532754000=20^{2}\times 12756598641331885. Rewrite the square root of the product \sqrt{20^{2}\times 12756598641331885} as the product of square roots \sqrt{20^{2}}\sqrt{12756598641331885}. Take the square root of 20^{2}.
120\sqrt{12756598641331885}
Multiply 6 and 20 to get 120.