Solve 5/3/sqrt{frac{28{9}}*2}

$$\frac { \frac { 5 } { 3 } } { \sqrt { \frac { 28 } { 9 } } \cdot 2 }$$

Evaluate

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

Solution Steps

Rewrite the square root of the division \sqrt{\frac{28}{9}} as the division of square roots \frac{\sqrt{28}}{\sqrt{9}}.

$$\frac{\frac{5}{3}}{2\times \frac{\sqrt{28}}{\sqrt{9}}}$$

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$\frac{\frac{5}{3}}{2\times \frac{2\sqrt{7}}{\sqrt{9}}}$$

Calculate the square root of 9 and get 3.

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

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.

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