Solve 21/4(1/sqrt{3})

$$\frac { 21 } { 4 } ( \frac { 1 } { \sqrt { 3 } } )$$

Evaluate

$$\frac{7\sqrt{3}}{4}\approx 3.031088913$$

Solution Steps

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{21}{4}\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{21}{4}\times \frac{\sqrt{3}}{3}$$

Multiply \frac{21}{4} times \frac{\sqrt{3}}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{21\sqrt{3}}{4\times 3}$$

Cancel out 3 in both numerator and denominator.

$$\frac{7\sqrt{3}}{4}$$