Evaluate
\frac{65\sqrt{17}+567}{256}\approx 3.261726038
Factor
\frac{65 \sqrt{17} + 567}{256} = 3.2617260377544843
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\frac{64\left(\sqrt{17}+9\right)}{256}-\frac{9-\sqrt{17}}{256}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 256 is 256. Multiply \frac{\sqrt{17}+9}{4} times \frac{64}{64}.
\frac{64\left(\sqrt{17}+9\right)-\left(9-\sqrt{17}\right)}{256}
Since \frac{64\left(\sqrt{17}+9\right)}{256} and \frac{9-\sqrt{17}}{256} have the same denominator, subtract them by subtracting their numerators.
\frac{64\sqrt{17}+576-9+\sqrt{17}}{256}
Do the multiplications in 64\left(\sqrt{17}+9\right)-\left(9-\sqrt{17}\right).
\frac{65\sqrt{17}+567}{256}
Do the calculations in 64\sqrt{17}+576-9+\sqrt{17}.
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