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

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

Evaluate

$$8\sqrt{3}+10\approx 23.856406461$$

Solution Steps

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

$$6\left(\sqrt{3}\right)^{2}-4\sqrt{3}+12\sqrt{3}-8$$

The square of \sqrt{3} is 3.

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

Multiply 6 and 3 to get 18.

$$18-4\sqrt{3}+12\sqrt{3}-8$$

Combine -4\sqrt{3} and 12\sqrt{3} to get 8\sqrt{3}.

$$18+8\sqrt{3}-8$$

Subtract 8 from 18 to get 10.

$$10+8\sqrt{3}$$

Factor

$$2 {(4 \sqrt{3} + 5)} = 23.856406461$$