Solve sqrt{72}*sqrt{1/12}

$$\sqrt { 72 } \times \sqrt { \frac { 1 } { 12 } }$$

Evaluate

$$\sqrt{6}\approx 2.449489743$$

Solution Steps

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

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

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

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

Calculate the square root of 1 and get 1.

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

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}.

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

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

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

The square of \sqrt{3} is 3.

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

Multiply 2 and 3 to get 6.

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

Cancel out 6 and 6.

$$\sqrt{3}\sqrt{2}$$

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

$$\sqrt{6}$$