Solve 2sqrt{1frac{1/2}}{5}sqrt{1/6}*sqrt{12}

$$\frac{ 2 \sqrt{ 1 \frac{ 1 }{ 2 } } }{ 5 } \sqrt{ \frac{ 1 }{ 6 } } \times \sqrt{ 12 }$$

Evaluate

$$\frac{2\sqrt{3}}{5}\approx 0.692820323$$

Solution Steps

Multiply 1 and 2 to get 2.

$$\frac{2\sqrt{\frac{2+1}{2}}}{5}\sqrt{\frac{1}{6}}\sqrt{12}$$

Add 2 and 1 to get 3.

$$\frac{2\sqrt{\frac{3}{2}}}{5}\sqrt{\frac{1}{6}}\sqrt{12}$$

Rewrite the square root of the division \sqrt{\frac{3}{2}} as the division of square roots \frac{\sqrt{3}}{\sqrt{2}}.

$$\frac{2\times \frac{\sqrt{3}}{\sqrt{2}}}{5}\sqrt{\frac{1}{6}}\sqrt{12}$$

Rationalize the denominator of \frac{\sqrt{3}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{2\times \frac{\sqrt{3}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}}{5}\sqrt{\frac{1}{6}}\sqrt{12}$$

The square of \sqrt{2} is 2.

$$\frac{2\times \frac{\sqrt{3}\sqrt{2}}{2}}{5}\sqrt{\frac{1}{6}}\sqrt{12}$$

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

$$\frac{2\times \frac{\sqrt{6}}{2}}{5}\sqrt{\frac{1}{6}}\sqrt{12}$$

Cancel out 2 and 2.

$$\frac{\sqrt{6}}{5}\sqrt{\frac{1}{6}}\sqrt{12}$$

Rewrite the square root of the division \sqrt{\frac{1}{6}} as the division of square roots \frac{\sqrt{1}}{\sqrt{6}}.

$$\frac{\sqrt{6}}{5}\times \frac{\sqrt{1}}{\sqrt{6}}\sqrt{12}$$

Calculate the square root of 1 and get 1.

$$\frac{\sqrt{6}}{5}\times \frac{1}{\sqrt{6}}\sqrt{12}$$

Rationalize the denominator of \frac{1}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{\sqrt{6}}{5}\times \frac{\sqrt{6}}{\left(\sqrt{6}\right)^{2}}\sqrt{12}$$

The square of \sqrt{6} is 6.

$$\frac{\sqrt{6}}{5}\times \frac{\sqrt{6}}{6}\sqrt{12}$$

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}.

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

Multiply \frac{\sqrt{6}}{5} times \frac{\sqrt{6}}{6} by multiplying numerator times numerator and denominator times denominator.

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

Express \frac{\sqrt{6}\sqrt{6}}{5\times 6}\times 2 as a single fraction.

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

Cancel out 2 in both numerator and denominator.

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

Express \frac{\sqrt{6}\sqrt{6}}{3\times 5}\sqrt{3} as a single fraction.

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

Multiply \sqrt{6} and \sqrt{6} to get 6.

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

Cancel out 3 in both numerator and denominator.

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