Solve 7/5/sqrt{3/4}

$$\frac { \frac { 7 } { 5 } } { \frac { \sqrt { 3 } } { 4 } }$$

Evaluate

$$\frac{28\sqrt{3}}{15}\approx 3.233161507$$

Solution Steps

Divide \frac{7}{5} by \frac{\sqrt{3}}{4} by multiplying \frac{7}{5} by the reciprocal of \frac{\sqrt{3}}{4}.

$$\frac{7\times 4}{5\sqrt{3}}$$

Multiply 7 and 4 to get 28.

$$\frac{28}{5\sqrt{3}}$$

Rationalize the denominator of \frac{28}{5\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{28\sqrt{3}}{5\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{28\sqrt{3}}{5\times 3}$$

Multiply 5 and 3 to get 15.

$$\frac{28\sqrt{3}}{15}$$