Solve sqrt{25*3/4}

$$\sqrt{ 25 \times \frac{ 3 }{ 4 } }$$

Evaluate

$$\frac{5\sqrt{3}}{2}\approx 4.330127019$$

Solution Steps

Express 25\times \frac{3}{4} as a single fraction.

$$\sqrt{\frac{25\times 3}{4}}$$

Multiply 25 and 3 to get 75.

$$\sqrt{\frac{75}{4}}$$

Rewrite the square root of the division \sqrt{\frac{75}{4}} as the division of square roots \frac{\sqrt{75}}{\sqrt{4}}.

$$\frac{\sqrt{75}}{\sqrt{4}}$$

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}.

$$\frac{5\sqrt{3}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{5\sqrt{3}}{2}$$