Solve sqrt{3}(sqrt{2}-sqrt{3})-sqrt{24}-3-sqrt{6}=

$$\sqrt{ 3 } ( \sqrt{ 2 } - \sqrt{ 3 } )- \sqrt{ 24 } -3- \sqrt{ 6 } =$$

Evaluate

$$-2\sqrt{6}-6\approx -10.898979486$$

Solution Steps

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

$$\sqrt{3}\sqrt{2}-\left(\sqrt{3}\right)^{2}-\sqrt{24}-3-\sqrt{6}$$

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

$$\sqrt{6}-\left(\sqrt{3}\right)^{2}-\sqrt{24}-3-\sqrt{6}$$

The square of \sqrt{3} is 3.

$$\sqrt{6}-3-\sqrt{24}-3-\sqrt{6}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

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

Combine \sqrt{6} and -2\sqrt{6} to get -\sqrt{6}.

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

Subtract 3 from -3 to get -6.

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

Combine -\sqrt{6} and -\sqrt{6} to get -2\sqrt{6}.

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