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

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

Evaluate

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

Solution Steps

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

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

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}.

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

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.

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