Solve 1/17(5/sqrt{16}-frac{sqrt{36}}{sqrt{24}})+2/5

$$\frac { 1 } { 17 } ( \frac { 5 } { \sqrt { 16 } } - \frac { \sqrt { 36 } } { \sqrt { 24 } } ) + \frac { 2 } { 5 }$$

Evaluate

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

Short Solution Steps

Calculate the square root of 16 and get 4.

$$\frac{1}{17}\left(\frac{5}{4}-\frac{\sqrt{36}}{\sqrt{24}}\right)+\frac{2}{5}$$

Calculate the square root of 36 and get 6.

$$\frac{1}{17}\left(\frac{5}{4}-\frac{6}{\sqrt{24}}\right)+\frac{2}{5}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$\frac{1}{17}\left(\frac{5}{4}-\frac{6}{2\sqrt{6}}\right)+\frac{2}{5}$$

Rationalize the denominator of \frac{6}{2\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{1}{17}\left(\frac{5}{4}-\frac{6\sqrt{6}}{2\left(\sqrt{6}\right)^{2}}\right)+\frac{2}{5}$$

The square of \sqrt{6} is 6.

$$\frac{1}{17}\left(\frac{5}{4}-\frac{6\sqrt{6}}{2\times 6}\right)+\frac{2}{5}$$

Cancel out 2\times 3 in both numerator and denominator.

$$\frac{1}{17}\left(\frac{5}{4}-\frac{\sqrt{6}}{2}\right)+\frac{2}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 2 is 4. Multiply \frac{\sqrt{6}}{2} times \frac{2}{2}.

$$\frac{1}{17}\left(\frac{5}{4}-\frac{2\sqrt{6}}{4}\right)+\frac{2}{5}$$

Since \frac{5}{4} and \frac{2\sqrt{6}}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{17}\times \frac{5-2\sqrt{6}}{4}+\frac{2}{5}$$

Multiply \frac{1}{17} times \frac{5-2\sqrt{6}}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5-2\sqrt{6}}{17\times 4}+\frac{2}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 17\times 4 and 5 is 340. Multiply \frac{5-2\sqrt{6}}{17\times 4} times \frac{5}{5}. Multiply \frac{2}{5} times \frac{68}{68}.

$$\frac{5\left(5-2\sqrt{6}\right)}{340}+\frac{2\times 68}{340}$$

Since \frac{5\left(5-2\sqrt{6}\right)}{340} and \frac{2\times 68}{340} have the same denominator, add them by adding their numerators.

$$\frac{5\left(5-2\sqrt{6}\right)+2\times 68}{340}$$

Do the multiplications in 5\left(5-2\sqrt{6}\right)+2\times 68.

$$\frac{25-10\sqrt{6}+136}{340}$$

Do the calculations in 25-10\sqrt{6}+136.

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

Factor

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