Solve frac{5/7sqrt{14}}{5/3}sqrt{7}

$$\frac{ \frac{ 5 }{ 7 } \sqrt{ 14 } }{ \frac{ 5 }{ 3 } } \sqrt{ 7 }$$

Evaluate

$$3\sqrt{2}\approx 4.242640687$$

Solution Steps

Divide \frac{5}{7}\sqrt{14} by \frac{5}{3} by multiplying \frac{5}{7}\sqrt{14} by the reciprocal of \frac{5}{3}.

$$\frac{\frac{5}{7}\sqrt{14}\times 3}{5}\sqrt{7}$$

Express \frac{5}{7}\times 3 as a single fraction.

$$\frac{\frac{5\times 3}{7}\sqrt{14}}{5}\sqrt{7}$$

Multiply 5 and 3 to get 15.

$$\frac{\frac{15}{7}\sqrt{14}}{5}\sqrt{7}$$

Divide \frac{15}{7}\sqrt{14} by 5 to get \frac{3}{7}\sqrt{14}.

$$\frac{3}{7}\sqrt{14}\sqrt{7}$$

Factor 14=7\times 2. Rewrite the square root of the product \sqrt{7\times 2} as the product of square roots \sqrt{7}\sqrt{2}.

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

Multiply \sqrt{7} and \sqrt{7} to get 7.

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

Cancel out 7 and 7.

$$3\sqrt{2}$$