Solve (2sqrt{2}-3sqrt{3})(6sqrt{2}-2sqrt{3})

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

Evaluate

$$42-22\sqrt{6}\approx -11.888774341$$

Solution Steps

Apply the distributive property by multiplying each term of 2\sqrt{2}-3\sqrt{3} by each term of 6\sqrt{2}-2\sqrt{3}.

$$12\left(\sqrt{2}\right)^{2}-4\sqrt{3}\sqrt{2}-18\sqrt{3}\sqrt{2}+6\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{2} is 2.

$$12\times 2-4\sqrt{3}\sqrt{2}-18\sqrt{3}\sqrt{2}+6\left(\sqrt{3}\right)^{2}$$

Multiply 12 and 2 to get 24.

$$24-4\sqrt{3}\sqrt{2}-18\sqrt{3}\sqrt{2}+6\left(\sqrt{3}\right)^{2}$$

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

$$24-4\sqrt{6}-18\sqrt{3}\sqrt{2}+6\left(\sqrt{3}\right)^{2}$$

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

$$24-4\sqrt{6}-18\sqrt{6}+6\left(\sqrt{3}\right)^{2}$$

Combine -4\sqrt{6} and -18\sqrt{6} to get -22\sqrt{6}.

$$24-22\sqrt{6}+6\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$24-22\sqrt{6}+6\times 3$$

Multiply 6 and 3 to get 18.

$$24-22\sqrt{6}+18$$

Add 24 and 18 to get 42.

$$42-22\sqrt{6}$$

Factor

$$2 {(21 - 11 \sqrt{6})} = -11.888774341$$