Solve 2/12-sqrt{6div3+58div2(8-6)8}

$$\frac { 2 } { 12 - \sqrt { 6 } \div 3 + 58 \div 2 ( 8 - 6 ) 8 }$$

Evaluate

$$\frac{\sqrt{6}+1428}{339863}\approx 0.0042089$$

Short Solution Steps

Divide 58 by 2 to get 29.

$$\frac{2}{12-\frac{\sqrt{6}}{3}+29\left(8-6\right)\times 8}$$

Subtract 6 from 8 to get 2.

$$\frac{2}{12-\frac{\sqrt{6}}{3}+29\times 2\times 8}$$

Multiply 29 and 2 to get 58.

$$\frac{2}{12-\frac{\sqrt{6}}{3}+58\times 8}$$

Multiply 58 and 8 to get 464.

$$\frac{2}{12-\frac{\sqrt{6}}{3}+464}$$

Add 12 and 464 to get 476.

$$\frac{2}{476-\frac{\sqrt{6}}{3}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 476 times \frac{3}{3}.

$$\frac{2}{\frac{476\times 3}{3}-\frac{\sqrt{6}}{3}}$$

Since \frac{476\times 3}{3} and \frac{\sqrt{6}}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{\frac{476\times 3-\sqrt{6}}{3}}$$

Do the multiplications in 476\times 3-\sqrt{6}.

$$\frac{2}{\frac{1428-\sqrt{6}}{3}}$$

Divide 2 by \frac{1428-\sqrt{6}}{3} by multiplying 2 by the reciprocal of \frac{1428-\sqrt{6}}{3}.

$$\frac{2\times 3}{1428-\sqrt{6}}$$

Rationalize the denominator of \frac{2\times 3}{1428-\sqrt{6}} by multiplying numerator and denominator by 1428+\sqrt{6}.

$$\frac{2\times 3\left(1428+\sqrt{6}\right)}{\left(1428-\sqrt{6}\right)\left(1428+\sqrt{6}\right)}$$

Consider \left(1428-\sqrt{6}\right)\left(1428+\sqrt{6}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{2\times 3\left(1428+\sqrt{6}\right)}{1428^{2}-\left(\sqrt{6}\right)^{2}}$$

Square 1428. Square \sqrt{6}.

$$\frac{2\times 3\left(1428+\sqrt{6}\right)}{2039184-6}$$

Subtract 6 from 2039184 to get 2039178.

$$\frac{2\times 3\left(1428+\sqrt{6}\right)}{2039178}$$

Multiply 2 and 3 to get 6.

$$\frac{6\left(1428+\sqrt{6}\right)}{2039178}$$

Divide 6\left(1428+\sqrt{6}\right) by 2039178 to get \frac{1}{339863}\left(1428+\sqrt{6}\right).

$$\frac{1}{339863}\left(1428+\sqrt{6}\right)$$

Use the distributive property to multiply \frac{1}{339863} by 1428+\sqrt{6}.

$$\frac{1}{339863}\times 1428+\frac{1}{339863}\sqrt{6}$$

Multiply \frac{1}{339863} and 1428 to get \frac{1428}{339863}.

$$\frac{1428}{339863}+\frac{1}{339863}\sqrt{6}$$