Solve sqrt{2}(4sqrt{6}-sqrt{3})

$$\sqrt { 2 } ( 4 \sqrt { 6 } - \sqrt { 3 } )$$

Evaluate

$$8\sqrt{3}-\sqrt{6}\approx 11.406916718$$

Solution Steps

Use the distributive property to multiply \sqrt{2} by 4\sqrt{6}-\sqrt{3}.

$$4\sqrt{2}\sqrt{6}-\sqrt{2}\sqrt{3}$$

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}.

$$4\sqrt{2}\sqrt{2}\sqrt{3}-\sqrt{2}\sqrt{3}$$

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

$$4\times 2\sqrt{3}-\sqrt{2}\sqrt{3}$$

Multiply 4 and 2 to get 8.

$$8\sqrt{3}-\sqrt{2}\sqrt{3}$$

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

$$8\sqrt{3}-\sqrt{6}$$