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

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

Evaluate

$$7\sqrt{6}+8\approx 25.146428199$$

Solution Steps

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

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

The square of \sqrt{3} is 3.

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

Multiply 4 and 3 to get 12.

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

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

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

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

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

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

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

The square of \sqrt{2} is 2.

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

Multiply -2 and 2 to get -4.

$$12+7\sqrt{6}-4$$

Subtract 4 from 12 to get 8.

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