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

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

Evaluate

$$\sqrt{6}-12\sqrt{2}\approx -14.521073006$$

Solution Steps

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

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

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

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

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

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

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

Multiply -4 and 3 to get -12.

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