Solve (6)sqrt{6}*sqrt{2/3}

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

Evaluate

$$12$$

Solution Steps

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

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

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

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

The square of \sqrt{3} is 3.

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

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

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

Cancel out 3, the greatest common factor in 6 and 3.

$$2\sqrt{6}\sqrt{6}$$

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

$$2\times 6$$

Multiply 2 and 6 to get 12.

$$12$$

Factor

$$2^{2}\times 3$$