Solve sqrt{3}(sqrt{2}+2)-sqrt{2}(sqrt{3}-1)

$$\sqrt{ 3 } ( \sqrt{ 2 } +2)- \sqrt{ 2 } ( \sqrt{ 3 } -1)$$

Evaluate

$$\sqrt{2}+2\sqrt{3}\approx 4.878315178$$

Solution Steps

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

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

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

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

Use the distributive property to multiply \sqrt{2} by \sqrt{3}-1.

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

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

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

To find the opposite of \sqrt{6}-\sqrt{2}, find the opposite of each term.

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

Combine \sqrt{6} and -\sqrt{6} to get 0.

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

The opposite of -\sqrt{2} is \sqrt{2}.

$$2\sqrt{3}+\sqrt{2}$$