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

$$2 \sqrt{ 12 } \times 4 \sqrt{ 3 } \div 5 \sqrt{ 2 }$$

Evaluate

$$\frac{48\sqrt{2}}{5}\approx 13.576450199$$

Solution Steps

Factor 12=3\times 4. Rewrite the square root of the product \sqrt{3\times 4} as the product of square roots \sqrt{3}\sqrt{4}.

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

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

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

Multiply 2 and 4 to get 8.

$$\frac{8\times 3\sqrt{4}}{5}\sqrt{2}$$

Multiply 8 and 3 to get 24.

$$\frac{24\sqrt{4}}{5}\sqrt{2}$$

Calculate the square root of 4 and get 2.

$$\frac{24\times 2}{5}\sqrt{2}$$

Multiply 24 and 2 to get 48.

$$\frac{48}{5}\sqrt{2}$$