Solve frac{(4+sqrt{3})(2sqrt{3}+2)}{12-4}

$$\frac { ( 4 + \sqrt { 3 } ) ( 2 \sqrt { 3 } + 2 ) } { 12 - 4 }$$

Evaluate

$$\frac{5\sqrt{3}+7}{4}\approx 3.915063509$$

Solution Steps

Subtract 4 from 12 to get 8.

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

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

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

The square of \sqrt{3} is 3.

$$\frac{8\sqrt{3}+8+2\times 3+2\sqrt{3}}{8}$$

Multiply 2 and 3 to get 6.

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

Add 8 and 6 to get 14.

$$\frac{8\sqrt{3}+14+2\sqrt{3}}{8}$$

Combine 8\sqrt{3} and 2\sqrt{3} to get 10\sqrt{3}.

$$\frac{10\sqrt{3}+14}{8}$$

Factor

$$\frac{5 \sqrt{3} + 7}{4} = 3.9150635094610964$$