Solve 5/3/2sqrt{7/3*2}

$$\frac { \frac { 5 } { 3 } } { \frac { 2 \sqrt { 7 } } { 3 } \cdot 2 }$$

Evaluate

$$\frac{5\sqrt{7}}{28}\approx 0.472455591$$

Solution Steps

Express 2\times \frac{2\sqrt{7}}{3} as a single fraction.

$$\frac{\frac{5}{3}}{\frac{2\times 2\sqrt{7}}{3}}$$

Divide \frac{5}{3} by \frac{2\times 2\sqrt{7}}{3} by multiplying \frac{5}{3} by the reciprocal of \frac{2\times 2\sqrt{7}}{3}.

$$\frac{5\times 3}{3\times 2\times 2\sqrt{7}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{5}{2\times 2\sqrt{7}}$$

Rationalize the denominator of \frac{5}{2\times 2\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{5\sqrt{7}}{2\times 2\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{5\sqrt{7}}{2\times 2\times 7}$$

Multiply 2 and 2 to get 4.

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

Multiply 4 and 7 to get 28.

$$\frac{5\sqrt{7}}{28}$$