Solve (3sqrt{2}-2sqrt{3})(4sqrt{2}+sqrt{3})

$$( 3 \sqrt { 2 } - 2 \sqrt { 3 } ) ( 4 \sqrt { 2 } + \sqrt { 3 } )$$

Evaluate

$$18-5\sqrt{6}\approx 5.752551286$$

Solution Steps

Apply the distributive property by multiplying each term of 3\sqrt{2}-2\sqrt{3} by each term of 4\sqrt{2}+\sqrt{3}.

$$12\left(\sqrt{2}\right)^{2}+3\sqrt{2}\sqrt{3}-8\sqrt{3}\sqrt{2}-2\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{2} is 2.

$$12\times 2+3\sqrt{2}\sqrt{3}-8\sqrt{3}\sqrt{2}-2\left(\sqrt{3}\right)^{2}$$

Multiply 12 and 2 to get 24.

$$24+3\sqrt{2}\sqrt{3}-8\sqrt{3}\sqrt{2}-2\left(\sqrt{3}\right)^{2}$$

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

$$24+3\sqrt{6}-8\sqrt{3}\sqrt{2}-2\left(\sqrt{3}\right)^{2}$$

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

$$24+3\sqrt{6}-8\sqrt{6}-2\left(\sqrt{3}\right)^{2}$$

Combine 3\sqrt{6} and -8\sqrt{6} to get -5\sqrt{6}.

$$24-5\sqrt{6}-2\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$24-5\sqrt{6}-2\times 3$$

Multiply -2 and 3 to get -6.

$$24-5\sqrt{6}-6$$

Subtract 6 from 24 to get 18.

$$18-5\sqrt{6}$$

Factor

$$18-5\sqrt{6}$$