Solve 2sqrt{12}*frac{sqrt{3}}{5}div3sqrt{2}

$$2 \sqrt { 12 } \times \frac { \sqrt { 3 } } { 5 } \div 3 \sqrt { 2 }$$

Evaluate

$$\frac{4\sqrt{2}}{5}\approx 1.13137085$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

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

Multiply 2 and 2 to get 4.

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

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

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

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

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

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

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

Express \frac{4\sqrt{3}\sqrt{3}}{5\times 3}\sqrt{2} as a single fraction.

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

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

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

Cancel out 3 in both numerator and denominator.

$$\frac{4\sqrt{2}}{5}$$