Solve frac{(9+sqrt{17})(5-sqrt{175})}{8}+2

$$\frac { ( 9 + \sqrt { 17 } ) ( 5 - \sqrt { 175 } ) } { 8 } + 2$$

Evaluate

$$\frac{5\sqrt{17}+61-5\sqrt{119}-45\sqrt{7}}{8}\approx -11.49835518$$

Short Solution Steps

Factor 175=5^{2}\times 7. Rewrite the square root of the product \sqrt{5^{2}\times 7} as the product of square roots \sqrt{5^{2}}\sqrt{7}. Take the square root of 5^{2}.

$$\frac{\left(9+\sqrt{17}\right)\left(5-5\sqrt{7}\right)}{8}+2$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{8}{8}.

$$\frac{\left(9+\sqrt{17}\right)\left(5-5\sqrt{7}\right)}{8}+\frac{2\times 8}{8}$$

Since \frac{\left(9+\sqrt{17}\right)\left(5-5\sqrt{7}\right)}{8} and \frac{2\times 8}{8} have the same denominator, add them by adding their numerators.

$$\frac{\left(9+\sqrt{17}\right)\left(5-5\sqrt{7}\right)+2\times 8}{8}$$

Do the multiplications in \left(9+\sqrt{17}\right)\left(5-5\sqrt{7}\right)+2\times 8.

$$\frac{45-45\sqrt{7}+5\sqrt{17}-5\sqrt{119}+16}{8}$$

Do the calculations in 45-45\sqrt{7}+5\sqrt{17}-5\sqrt{119}+16.

$$\frac{61-5\sqrt{119}-45\sqrt{7}+5\sqrt{17}}{8}$$

Factor

$$\frac{5 \sqrt{17} + 61 - 5 \sqrt{119} - 45 \sqrt{7}}{8} = -11.498355180374606$$