Solve 5/68-3/17sqrt{6}+2/5

$$\frac { 5 } { 68 } - \frac { 3 } { 17 \sqrt { 6 } } + \frac { 2 } { 5 }$$

Evaluate

$$-\frac{\sqrt{6}}{34}+\frac{161}{340}\approx 0.401485596$$

Short Solution Steps

Rationalize the denominator of \frac{3}{17\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{5}{68}-\frac{3\sqrt{6}}{17\left(\sqrt{6}\right)^{2}}+\frac{2}{5}$$

The square of \sqrt{6} is 6.

$$\frac{5}{68}-\frac{3\sqrt{6}}{17\times 6}+\frac{2}{5}$$

Cancel out 3 in both numerator and denominator.

$$\frac{5}{68}-\frac{\sqrt{6}}{2\times 17}+\frac{2}{5}$$

Multiply 2 and 17 to get 34.

$$\frac{5}{68}-\frac{\sqrt{6}}{34}+\frac{2}{5}$$

Least common multiple of 68 and 5 is 340. Convert \frac{5}{68} and \frac{2}{5} to fractions with denominator 340.

$$\frac{25}{340}-\frac{\sqrt{6}}{34}+\frac{136}{340}$$

Since \frac{25}{340} and \frac{136}{340} have the same denominator, add them by adding their numerators.

$$\frac{25+136}{340}-\frac{\sqrt{6}}{34}$$

Add 25 and 136 to get 161.

$$\frac{161}{340}-\frac{\sqrt{6}}{34}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 340 and 34 is 340. Multiply \frac{\sqrt{6}}{34} times \frac{10}{10}.

$$\frac{161}{340}-\frac{10\sqrt{6}}{340}$$

Since \frac{161}{340} and \frac{10\sqrt{6}}{340} have the same denominator, subtract them by subtracting their numerators.

$$\frac{161-10\sqrt{6}}{340}$$

Factor

$$\frac{161 - 10 \sqrt{6}}{340} = 0.4014855958004948$$