Solve (2sqrt{3}-sqrt{6})*sqrt{12}

$$( 2 \sqrt { 3 } - \sqrt { 6 } ) \times \sqrt { 12 }$$

Evaluate

$$12-6\sqrt{2}\approx 3.514718626$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

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

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

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

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

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

The square of \sqrt{3} is 3.

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

Multiply 4 and 3 to get 12.

$$12-2\sqrt{6}\sqrt{3}$$

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}.

$$12-2\sqrt{3}\sqrt{2}\sqrt{3}$$

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

$$12-2\times 3\sqrt{2}$$

Multiply -2 and 3 to get -6.

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