Solve 5sqrt{7}:7sqrt{2}*sqrt{14}

$$5 \sqrt { 7 } : 7 \sqrt { 2 } \times \sqrt { 14 }$$

Evaluate

$$10$$

Solution Steps

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

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

Express \frac{5\sqrt{7}}{7}\times 2 as a single fraction.

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

Express \frac{5\sqrt{7}\times 2}{7}\sqrt{7} as a single fraction.

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

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

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

Cancel out 7 and 7.

$$5\times 2$$

Multiply 5 and 2 to get 10.

$$10$$

Factor

$$2\times 5$$