Solve 1/4sqrt{3}div5sqrt{2}*2sqrt{12}

$$\frac { 1 } { 4 } \sqrt { 3 } \div 5 \sqrt { 2 } \cdot 2 \sqrt { 12 }$$

Evaluate

$$\frac{3\sqrt{2}}{5}\approx 0.848528137$$

Solution Steps

Factor 12=2\times 6. Rewrite the square root of the product \sqrt{2\times 6} as the product of square roots \sqrt{2}\sqrt{6}.

$$2\times \frac{\frac{1}{4}\sqrt{3}}{5}\sqrt{2}\sqrt{2}\sqrt{6}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$2\times \frac{\frac{1}{4}\sqrt{3}}{5}\times 2\sqrt{6}$$

Divide \frac{1}{4}\sqrt{3} by 5 to get \frac{1}{20}\sqrt{3}.

$$2\times \frac{1}{20}\sqrt{3}\times 2\sqrt{6}$$

Multiply 2 and \frac{1}{20} to get \frac{2}{20}.

$$\frac{2}{20}\sqrt{3}\times 2\sqrt{6}$$

Reduce the fraction \frac{2}{20} to lowest terms by extracting and canceling out 2.

$$\frac{1}{10}\sqrt{3}\times 2\sqrt{6}$$

Multiply \frac{1}{10} and 2 to get \frac{2}{10}.

$$\frac{2}{10}\sqrt{3}\sqrt{6}$$

Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\frac{1}{5}\sqrt{3}\sqrt{6}$$

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

$$\frac{1}{5}\sqrt{3}\sqrt{3}\sqrt{2}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{1}{5}\times 3\sqrt{2}$$

Multiply \frac{1}{5} and 3 to get \frac{3}{5}.

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