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

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

Evaluate

$$8-7\sqrt{6}\approx -9.146428199$$

Solution Steps

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

$$\sqrt{3}\sqrt{2}+4\left(\sqrt{3}\right)^{2}-2\left(\sqrt{2}\right)^{2}-8\sqrt{3}\sqrt{2}$$

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

$$\sqrt{6}+4\left(\sqrt{3}\right)^{2}-2\left(\sqrt{2}\right)^{2}-8\sqrt{3}\sqrt{2}$$

The square of \sqrt{3} is 3.

$$\sqrt{6}+4\times 3-2\left(\sqrt{2}\right)^{2}-8\sqrt{3}\sqrt{2}$$

Multiply 4 and 3 to get 12.

$$\sqrt{6}+12-2\left(\sqrt{2}\right)^{2}-8\sqrt{3}\sqrt{2}$$

The square of \sqrt{2} is 2.

$$\sqrt{6}+12-2\times 2-8\sqrt{3}\sqrt{2}$$

Multiply -2 and 2 to get -4.

$$\sqrt{6}+12-4-8\sqrt{3}\sqrt{2}$$

Subtract 4 from 12 to get 8.

$$\sqrt{6}+8-8\sqrt{3}\sqrt{2}$$

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

$$\sqrt{6}+8-8\sqrt{6}$$

Combine \sqrt{6} and -8\sqrt{6} to get -7\sqrt{6}.

$$-7\sqrt{6}+8$$