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

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

Evaluate

$$4-6\sqrt{3}\approx -6.392304845$$

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

Multiply 2 and 2 to get 4.

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

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}.

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

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

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

Multiply -3 and 2 to get -6.

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