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

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

Evaluate

$$2\left(\sqrt{6}-3\right)\approx -1.101020514$$

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}.

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

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

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

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

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

The square of \sqrt{3} is 3.

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

Multiply -2 and 3 to get -6.

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