Solve 52/sqrt{3}2*(2divsqrt{3}*2)

$$\frac{ 52 }{ \sqrt{ 3 } } 2 \times (2 \div \sqrt{ 3 } \times 2)$$

Evaluate

$$\frac{416}{3}\approx 138.666666667$$

Solution Steps

Rationalize the denominator of \frac{52}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$2\times \frac{52\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\times 2\times \frac{2}{\sqrt{3}}$$

The square of \sqrt{3} is 3.

$$2\times \frac{52\sqrt{3}}{3}\times 2\times \frac{2}{\sqrt{3}}$$

Multiply 2 and 2 to get 4.

$$4\times \frac{52\sqrt{3}}{3}\times \frac{2}{\sqrt{3}}$$

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

$$4\times \frac{52\sqrt{3}}{3}\times \frac{2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$4\times \frac{52\sqrt{3}}{3}\times \frac{2\sqrt{3}}{3}$$

Express 4\times \frac{52\sqrt{3}}{3} as a single fraction.

$$\frac{4\times 52\sqrt{3}}{3}\times \frac{2\sqrt{3}}{3}$$

Multiply \frac{4\times 52\sqrt{3}}{3} times \frac{2\sqrt{3}}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 52\sqrt{3}\times 2\sqrt{3}}{3\times 3}$$

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

$$\frac{4\times 52\times 3\times 2}{3\times 3}$$

Cancel out 3 in both numerator and denominator.

$$\frac{2\times 4\times 52}{3}$$

Multiply 2 and 4 to get 8.

$$\frac{8\times 52}{3}$$

Multiply 8 and 52 to get 416.

$$\frac{416}{3}$$

Factor

$$\frac{2 ^ {5} \cdot 13}{3} = 138\frac{2}{3} = 138.66666666666666$$