Solve sqrt{3}*(sqrt{2}-sqrt{3})-sqrt{24}-1

$$\sqrt{ 3 } \times ( \sqrt{ 2 } - \sqrt{ 3 } )- \sqrt{ 24 } -1$$

Evaluate

$$-\sqrt{6}-4\approx -6.449489743$$

Solution Steps

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

$$\sqrt{3}\sqrt{2}-\left(\sqrt{3}\right)^{2}-\sqrt{24}-1$$

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

$$\sqrt{6}-\left(\sqrt{3}\right)^{2}-\sqrt{24}-1$$

The square of \sqrt{3} is 3.

$$\sqrt{6}-3-\sqrt{24}-1$$

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}.

$$\sqrt{6}-3-2\sqrt{6}-1$$

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

$$-\sqrt{6}-3-1$$

Subtract 1 from -3 to get -4.

$$-\sqrt{6}-4$$