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

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

Evaluate

$$6\left(\sqrt{2}-1\right)\approx 2.485281374$$

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}.

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

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

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

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

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

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}.

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

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

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

Multiply 2 and 3 to get 6.

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

The square of \sqrt{3} is 3.

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

Multiply -2 and 3 to get -6.

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