Solve (2)(4sqrt{2}-3sqrt{6})div2sqrt{3}

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

Evaluate

$$4\sqrt{6}-9\sqrt{2}\approx -2.92996309$$

Solution Steps

Cancel out 2 and 2.

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

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

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

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

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

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}.

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

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

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

Multiply -3 and 3 to get -9.

$$4\sqrt{6}-9\sqrt{2}$$