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

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

Evaluate

$$\frac{9\sqrt{2}}{10}\approx 1.272792206$$

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}.

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

Multiply 3 and 2 to get 6.

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

Express 6\times \frac{\sqrt{3}}{4} as a single fraction.

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

Divide 6\sqrt{3} by 4 to get \frac{3}{2}\sqrt{3}.

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

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

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

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

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

Multiply 3 and 3 to get 9.

$$\frac{\frac{9}{2}}{5}\sqrt{2}$$

Express \frac{\frac{9}{2}}{5} as a single fraction.

$$\frac{9}{2\times 5}\sqrt{2}$$

Multiply 2 and 5 to get 10.

$$\frac{9}{10}\sqrt{2}$$