Solve (6/sqrt{3})^2

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

Evaluate

$$12$$

Solution Steps

Rationalize the denominator of \frac{6}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Divide 6\sqrt{3} by 3 to get 2\sqrt{3}.

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

Expand \left(2\sqrt{3}\right)^{2}.

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

Calculate 2 to the power of 2 and get 4.

$$4\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$4\times 3$$

Multiply 4 and 3 to get 12.

$$12$$

Factor

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