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\frac{\sqrt{53264}}{\sqrt{38025}}
Rewrite the square root of the division \sqrt{\frac{53264}{38025}} as the division of square roots \frac{\sqrt{53264}}{\sqrt{38025}}.
\frac{4\sqrt{3329}}{\sqrt{38025}}
Factor 53264=4^{2}\times 3329. Rewrite the square root of the product \sqrt{4^{2}\times 3329} as the product of square roots \sqrt{4^{2}}\sqrt{3329}. Take the square root of 4^{2}.
\frac{4\sqrt{3329}}{195}
Calculate the square root of 38025 and get 195.