Solve 0.2*sqrt{2}*0.2*sqrt{6}

$$0.2 \times \sqrt { 2 } \times 0.2 \times \sqrt { 6 }$$

Evaluate

$$\frac{2\sqrt{3}}{25}\approx 0.138564065$$

Solution Steps

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$0.2\times 0.2\sqrt{2}\sqrt{2}\sqrt{3}$$

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

$$0.2\times 0.2\times 2\sqrt{3}$$

Multiply 0.2 and 0.2 to get 0.04.

$$0.04\times 2\sqrt{3}$$

Multiply 0.04 and 2 to get 0.08.

$$0.08\sqrt{3}$$