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

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

Evaluate

$$18-7\sqrt{6}\approx 0.853571801$$

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

Multiply 6 and 2 to get 12.

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

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

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

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

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

Combine -4\sqrt{6} and -3\sqrt{6} to get -7\sqrt{6}.

$$12-7\sqrt{6}+2\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$12-7\sqrt{6}+2\times 3$$

Multiply 2 and 3 to get 6.

$$12-7\sqrt{6}+6$$

Add 12 and 6 to get 18.

$$18-7\sqrt{6}$$

Factor

$$18-7\sqrt{6}$$