Solve 3/4sqrt{75}

$$\frac { 3 } { 4 } \sqrt { 75 }$$

Evaluate

$$\frac{15\sqrt{3}}{4}\approx 6.495190528$$

Solution Steps

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}.

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

Express \frac{3}{4}\times 5 as a single fraction.

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

Multiply 3 and 5 to get 15.

$$\frac{15}{4}\sqrt{3}$$