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\sqrt{\frac{25\times 3}{4}}
Express 25\times \frac{3}{4} as a single fraction.
\sqrt{\frac{75}{4}}
Multiply 25 and 3 to get 75.
\frac{\sqrt{75}}{\sqrt{4}}
Rewrite the square root of the division \sqrt{\frac{75}{4}} as the division of square roots \frac{\sqrt{75}}{\sqrt{4}}.
\frac{5\sqrt{3}}{\sqrt{4}}
Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.
\frac{5\sqrt{3}}{2}
Calculate the square root of 4 and get 2.