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

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

Evaluate

$$13\sqrt{6}-18\approx 13.843366656$$

Solution Steps

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

$$12\sqrt{3}\sqrt{2}-3\left(\sqrt{2}\right)^{2}-4\left(\sqrt{3}\right)^{2}+\sqrt{3}\sqrt{2}$$

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

$$12\sqrt{6}-3\left(\sqrt{2}\right)^{2}-4\left(\sqrt{3}\right)^{2}+\sqrt{3}\sqrt{2}$$

The square of \sqrt{2} is 2.

$$12\sqrt{6}-3\times 2-4\left(\sqrt{3}\right)^{2}+\sqrt{3}\sqrt{2}$$

Multiply -3 and 2 to get -6.

$$12\sqrt{6}-6-4\left(\sqrt{3}\right)^{2}+\sqrt{3}\sqrt{2}$$

The square of \sqrt{3} is 3.

$$12\sqrt{6}-6-4\times 3+\sqrt{3}\sqrt{2}$$

Multiply -4 and 3 to get -12.

$$12\sqrt{6}-6-12+\sqrt{3}\sqrt{2}$$

Subtract 12 from -6 to get -18.

$$12\sqrt{6}-18+\sqrt{3}\sqrt{2}$$

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

$$12\sqrt{6}-18+\sqrt{6}$$

Combine 12\sqrt{6} and \sqrt{6} to get 13\sqrt{6}.

$$13\sqrt{6}-18$$

Factor

$$13 \sqrt{6} - 18 = 13.843366656$$