Solve 4/sqrt{3/2}

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

Evaluate

$$\frac{8\sqrt{3}}{3}\approx 4.618802154$$

Solution Steps

Divide 4 by \frac{\sqrt{3}}{2} by multiplying 4 by the reciprocal of \frac{\sqrt{3}}{2}.

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

Multiply 4 and 2 to get 8.

$$\frac{8}{\sqrt{3}}$$

Rationalize the denominator of \frac{8}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{8\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{8\sqrt{3}}{3}$$