Solve 1(2/7)*sqrt{2}*sqrt{10}

$$1 ( \frac { 2 } { 7 } ) \times \sqrt { 2 } \times \sqrt { 10 }$$

Evaluate

$$\frac{4\sqrt{5}}{7}\approx 1.27775313$$

Solution Steps

Factor 10=2\times 5. Rewrite the square root of the product \sqrt{2\times 5} as the product of square roots \sqrt{2}\sqrt{5}.

$$1\times \frac{2}{7}\sqrt{2}\sqrt{2}\sqrt{5}$$

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

$$1\times \frac{2}{7}\times 2\sqrt{5}$$

Multiply 1 and \frac{2}{7} to get \frac{2}{7}.

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

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

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

Multiply 2 and 2 to get 4.

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