Solve left(3sqrt{2}-1right)left(sqrt{3}-sqrt{2}right)

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

Evaluate

$$\sqrt{2}+3\sqrt{6}-\sqrt{3}-6\approx 1.030631983$$

Solution Steps

Apply the distributive property by multiplying each term of 3\sqrt{2}-1 by each term of \sqrt{3}-\sqrt{2}.

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

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

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

The square of \sqrt{2} is 2.

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

Multiply -3 and 2 to get -6.

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