Solve 2sqrt{2}(3sqrt{6}-sqrt{3})

$$2 \sqrt { 2 } ( 3 \sqrt { 6 } - \sqrt { 3 } )$$

Evaluate

$$2\sqrt{6}\left(3\sqrt{2}-1\right)\approx 15.885630205$$

Solution Steps

Use the distributive property to multiply 2\sqrt{2} by 3\sqrt{6}-\sqrt{3}.

$$6\sqrt{2}\sqrt{6}-2\sqrt{3}\sqrt{2}$$

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}.

$$6\sqrt{2}\sqrt{2}\sqrt{3}-2\sqrt{3}\sqrt{2}$$

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

$$6\times 2\sqrt{3}-2\sqrt{3}\sqrt{2}$$

Multiply 6 and 2 to get 12.

$$12\sqrt{3}-2\sqrt{3}\sqrt{2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$12\sqrt{3}-2\sqrt{6}$$

Factor

$$2 \sqrt{6} {(\sqrt{3} \sqrt{6} - 1)} = 15.885630205$$