Solve (2sqrt{2}-8sqrt{3})(sqrt{2}-sqrt{3})=

$$( 2 \sqrt { 2 } - 8 \sqrt { 3 } ) ( \sqrt { 2 } - \sqrt { 3 } ) =$$

Evaluate

$$28-10\sqrt{6}\approx 3.505102572$$

Solution Steps

Apply the distributive property by multiplying each term of 2\sqrt{2}-8\sqrt{3} by each term of \sqrt{2}-\sqrt{3}.

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

The square of \sqrt{2} is 2.

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

Multiply 2 and 2 to get 4.

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

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

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

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

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

Combine -2\sqrt{6} and -8\sqrt{6} to get -10\sqrt{6}.

$$4-10\sqrt{6}+8\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$4-10\sqrt{6}+8\times 3$$

Multiply 8 and 3 to get 24.

$$4-10\sqrt{6}+24$$

Add 4 and 24 to get 28.

$$28-10\sqrt{6}$$

Factor

$$2 {(14 - 5 \sqrt{6})} = 3.505102572$$