Solve 2sqrt{2}*frac{sqrt{3}}{4}div5sqrt{2}

$$2 \sqrt { 2 } \times \frac { \sqrt { 3 } } { 4 } \div 5 \sqrt { 2 }$$

Evaluate

$$\frac{\sqrt{3}}{5}\approx 0.346410162$$

Solution Steps

Cancel out 4, the greatest common factor in 2 and 4.

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

Express \frac{\sqrt{3}}{2}\sqrt{2} as a single fraction.

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

Express \frac{\frac{\sqrt{3}\sqrt{2}}{2}}{5} as a single fraction.

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

Express \frac{\sqrt{3}\sqrt{2}}{2\times 5}\sqrt{2} as a single fraction.

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

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

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

Cancel out 2 in both numerator and denominator.

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