Solve 6div((sqrt{3}div3)*2*2)

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

Evaluate

$$\frac{3\sqrt{3}}{2}\approx 2.598076211$$

Solution Steps

Multiply 2 and 2 to get 4.

$$\frac{6}{4\times \frac{\sqrt{3}}{3}}$$

Express 4\times \frac{\sqrt{3}}{3} as a single fraction.

$$\frac{6}{\frac{4\sqrt{3}}{3}}$$

Divide 6 by \frac{4\sqrt{3}}{3} by multiplying 6 by the reciprocal of \frac{4\sqrt{3}}{3}.

$$\frac{6\times 3}{4\sqrt{3}}$$

Cancel out 2 in both numerator and denominator.

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

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

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

The square of \sqrt{3} is 3.

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

Multiply 3 and 3 to get 9.

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

Multiply 2 and 3 to get 6.

$$\frac{9\sqrt{3}}{6}$$

Divide 9\sqrt{3} by 6 to get \frac{3}{2}\sqrt{3}.

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