Solve (10+8sqrt{3}+4)*81/2-10+6sqrt{3}+4)*6*1/2

$$( 10 + 8 \sqrt { 3 } + 4 ) \times 8 \frac { 1 } { 2 } - 10 + 6 \sqrt { 3 } + 4 ) \times 6 \times \frac { 1 } { 2 }$$

Evaluate

$$74\sqrt{3}+113\approx 241.17175976$$

Solution Steps

Add 10 and 4 to get 14.

$$\left(14+8\sqrt{3}\right)\times \frac{8\times 2+1}{2}-10+6\sqrt{3}+4$$

Multiply 8 and 2 to get 16.

$$\left(14+8\sqrt{3}\right)\times \frac{16+1}{2}-10+6\sqrt{3}+4$$

Add 16 and 1 to get 17.

$$\left(14+8\sqrt{3}\right)\times \frac{17}{2}-10+6\sqrt{3}+4$$

Use the distributive property to multiply 14+8\sqrt{3} by \frac{17}{2}.

$$14\times \frac{17}{2}+8\sqrt{3}\times \frac{17}{2}-10+6\sqrt{3}+4$$

Express 14\times \frac{17}{2} as a single fraction.

$$\frac{14\times 17}{2}+8\sqrt{3}\times \frac{17}{2}-10+6\sqrt{3}+4$$

Multiply 14 and 17 to get 238.

$$\frac{238}{2}+8\sqrt{3}\times \frac{17}{2}-10+6\sqrt{3}+4$$

Divide 238 by 2 to get 119.

$$119+8\sqrt{3}\times \frac{17}{2}-10+6\sqrt{3}+4$$

Express 8\times \frac{17}{2} as a single fraction.

$$119+\frac{8\times 17}{2}\sqrt{3}-10+6\sqrt{3}+4$$

Multiply 8 and 17 to get 136.

$$119+\frac{136}{2}\sqrt{3}-10+6\sqrt{3}+4$$

Divide 136 by 2 to get 68.

$$119+68\sqrt{3}-10+6\sqrt{3}+4$$

Subtract 10 from 119 to get 109.

$$109+68\sqrt{3}+6\sqrt{3}+4$$

Combine 68\sqrt{3} and 6\sqrt{3} to get 74\sqrt{3}.

$$109+74\sqrt{3}+4$$

Add 109 and 4 to get 113.

$$113+74\sqrt{3}$$