Solve 3/4sqrt{363}

$$\frac { 3 } { 4 } \sqrt { 363 }$$

Evaluate

$$\frac{33\sqrt{3}}{4}\approx 14.289419162$$

Solution Steps

Factor 363=11^{2}\times 3. Rewrite the square root of the product \sqrt{11^{2}\times 3} as the product of square roots \sqrt{11^{2}}\sqrt{3}. Take the square root of 11^{2}.

$$\frac{3}{4}\times 11\sqrt{3}$$

Express \frac{3}{4}\times 11 as a single fraction.

$$\frac{3\times 11}{4}\sqrt{3}$$

Multiply 3 and 11 to get 33.

$$\frac{33}{4}\sqrt{3}$$