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

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

Evaluate

$$4\sqrt{6}\left(2\sqrt{3}-1\right)\approx 24.143166526$$

Solution Steps

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

$$8\sqrt{3}\sqrt{6}-4\sqrt{3}\sqrt{2}$$

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}.

$$8\sqrt{3}\sqrt{3}\sqrt{2}-4\sqrt{3}\sqrt{2}$$

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

$$8\times 3\sqrt{2}-4\sqrt{3}\sqrt{2}$$

Multiply 8 and 3 to get 24.

$$24\sqrt{2}-4\sqrt{3}\sqrt{2}$$

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

$$24\sqrt{2}-4\sqrt{6}$$

Factor

$$4 \sqrt{6} {(\sqrt{2} \sqrt{6} - 1)} = 24.143166526$$