Solve (2/7)*sqrt{2}*sqrt{18}

$$( \frac{ 2 }{ 7 } ) \times \sqrt{ 2 } \times \sqrt{ 18 }$$

Evaluate

$$\frac{12}{7}\approx 1.714285714$$

Solution Steps

Factor 18=2\times 9. Rewrite the square root of the product \sqrt{2\times 9} as the product of square roots \sqrt{2}\sqrt{9}.

$$\frac{2}{7}\sqrt{2}\sqrt{2}\sqrt{9}$$

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

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

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

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

Multiply 2 and 2 to get 4.

$$\frac{4}{7}\sqrt{9}$$

Calculate the square root of 9 and get 3.

$$\frac{4}{7}\times 3$$

Express \frac{4}{7}\times 3 as a single fraction.

$$\frac{4\times 3}{7}$$

Multiply 4 and 3 to get 12.

$$\frac{12}{7}$$

Factor

$$\frac{2 ^ {2} \cdot 3}{7} = 1\frac{5}{7} = 1.7142857142857142$$