Solve (sqrt{18}-2sqrt{2})*sqrt{1/12}

$$( \sqrt { 18 } - 2 \sqrt { 2 } ) \cdot \sqrt { \frac { 1 } { 12 } }$$

Evaluate

$$\frac{\sqrt{6}}{6}\approx 0.40824829$$

Solution Steps

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$\left(3\sqrt{2}-2\sqrt{2}\right)\sqrt{\frac{1}{12}}$$

Combine 3\sqrt{2} and -2\sqrt{2} to get \sqrt{2}.

$$\sqrt{2}\sqrt{\frac{1}{12}}$$

Rewrite the square root of the division \sqrt{\frac{1}{12}} as the division of square roots \frac{\sqrt{1}}{\sqrt{12}}.

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

Calculate the square root of 1 and get 1.

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

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}.

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

Rationalize the denominator of \frac{1}{2\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Multiply 2 and 3 to get 6.

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

Express \sqrt{2}\times \frac{\sqrt{3}}{6} as a single fraction.

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

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

$$\frac{\sqrt{6}}{6}$$