Solve 8+4(3)(7-4/3)(2+sqrt{3})

$$8 + 4 ( 3 ) ( 7 - 4 / 3 ) ( 2 + \sqrt { 3 } )$$

Evaluate

$$68\sqrt{3}+144\approx 261.779454915$$

Solution Steps

Multiply 4 and 3 to get 12.

$$8+12\left(7-\frac{4}{3}\right)\left(2+\sqrt{3}\right)$$

Convert 7 to fraction \frac{21}{3}.

$$8+12\left(\frac{21}{3}-\frac{4}{3}\right)\left(2+\sqrt{3}\right)$$

Since \frac{21}{3} and \frac{4}{3} have the same denominator, subtract them by subtracting their numerators.

$$8+12\times \frac{21-4}{3}\left(2+\sqrt{3}\right)$$

Subtract 4 from 21 to get 17.

$$8+12\times \frac{17}{3}\left(2+\sqrt{3}\right)$$

Express 12\times \frac{17}{3} as a single fraction.

$$8+\frac{12\times 17}{3}\left(2+\sqrt{3}\right)$$

Multiply 12 and 17 to get 204.

$$8+\frac{204}{3}\left(2+\sqrt{3}\right)$$

Divide 204 by 3 to get 68.

$$8+68\left(2+\sqrt{3}\right)$$

Use the distributive property to multiply 68 by 2+\sqrt{3}.

$$8+136+68\sqrt{3}$$

Add 8 and 136 to get 144.

$$144+68\sqrt{3}$$

Factor

$$4 {(17 \sqrt{3} + 36)} = 261.779454915$$