Solve 3/4sqrt{392}

$$\frac { 3 } { 4 } \sqrt { 392 }$$

Evaluate

$$\frac{21\sqrt{2}}{2}\approx 14.849242405$$

Solution Steps

Factor 392=14^{2}\times 2. Rewrite the square root of the product \sqrt{14^{2}\times 2} as the product of square roots \sqrt{14^{2}}\sqrt{2}. Take the square root of 14^{2}.

$$\frac{3}{4}\times 14\sqrt{2}$$

Express \frac{3}{4}\times 14 as a single fraction.

$$\frac{3\times 14}{4}\sqrt{2}$$

Multiply 3 and 14 to get 42.

$$\frac{42}{4}\sqrt{2}$$

Reduce the fraction \frac{42}{4} to lowest terms by extracting and canceling out 2.

$$\frac{21}{2}\sqrt{2}$$