Solve frac{3sqrt{3}}{frac{sqrt{3}}{3}}*frac{2sqrt{3}}{3}

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

Evaluate

$$6\sqrt{3}\approx 10.392304845$$

Solution Steps

Divide 3\sqrt{3} by \frac{\sqrt{3}}{3} by multiplying 3\sqrt{3} by the reciprocal of \frac{\sqrt{3}}{3}.

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

Multiply 3 and 3 to get 9.

$$\frac{9\sqrt{3}}{\sqrt{3}}\times \frac{2\sqrt{3}}{3}$$

Rationalize the denominator of \frac{9\sqrt{3}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{9\sqrt{3}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\times \frac{2\sqrt{3}}{3}$$

The square of \sqrt{3} is 3.

$$\frac{9\sqrt{3}\sqrt{3}}{3}\times \frac{2\sqrt{3}}{3}$$

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

$$\frac{9\times 3}{3}\times \frac{2\sqrt{3}}{3}$$

Multiply 9 and 3 to get 27.

$$\frac{27}{3}\times \frac{2\sqrt{3}}{3}$$

Divide 27 by 3 to get 9.

$$9\times \frac{2\sqrt{3}}{3}$$

Cancel out 3, the greatest common factor in 9 and 3.

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

Multiply 3 and 2 to get 6.

$$6\sqrt{3}$$