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

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

Evaluate

$$5\sqrt{6}\approx 12.247448714$$

Solution Steps

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

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

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

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

The square of \sqrt{2} is 2.

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

Multiply -3 and 2 to get -6.

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

The square of \sqrt{3} is 3.

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

Multiply 2 and 3 to get 6.

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

Add -6 and 6 to get 0.

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

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

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

Combine 6\sqrt{6} and -\sqrt{6} to get 5\sqrt{6}.

$$5\sqrt{6}$$