Solve 2sqrt{12}*frac{sqrt{3}}{4}*1/sqrt{50}

$$2 \sqrt { 12 } \times \frac { \sqrt { 3 } } { 4 } \times \frac { 1 } { \sqrt { 50 } }$$

Evaluate

$$\frac{3\sqrt{2}}{10}\approx 0.424264069$$

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}.

$$2\times 2\sqrt{3}\times \frac{\sqrt{3}}{4}\times \frac{1}{\sqrt{50}}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{3}\times \frac{\sqrt{3}}{4}\times \frac{1}{\sqrt{50}}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

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

Rationalize the denominator of \frac{1}{5\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$4\sqrt{3}\times \frac{\sqrt{3}}{4}\times \frac{\sqrt{2}}{5\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

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

Multiply 5 and 2 to get 10.

$$4\sqrt{3}\times \frac{\sqrt{3}}{4}\times \frac{\sqrt{2}}{10}$$

Cancel out 4 and 4.

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

Express \sqrt{3}\times \frac{\sqrt{2}}{10} as a single fraction.

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

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

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

Express \frac{\sqrt{6}}{10}\sqrt{3} as a single fraction.

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

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}.

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

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

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