Solve sqrt{625-(8+121/17)}

$$\sqrt { 625 - ( 8 + \frac { 121 } { 17 } ) }$$

Evaluate

$$\frac{72\sqrt{34}}{17}\approx 24.695796261$$

Solution Steps

Convert 8 to fraction \frac{136}{17}.

$$\sqrt{625-\left(\frac{136}{17}+\frac{121}{17}\right)}$$

Since \frac{136}{17} and \frac{121}{17} have the same denominator, add them by adding their numerators.

$$\sqrt{625-\frac{136+121}{17}}$$

Add 136 and 121 to get 257.

$$\sqrt{625-\frac{257}{17}}$$

Convert 625 to fraction \frac{10625}{17}.

$$\sqrt{\frac{10625}{17}-\frac{257}{17}}$$

Since \frac{10625}{17} and \frac{257}{17} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{10625-257}{17}}$$

Subtract 257 from 10625 to get 10368.

$$\sqrt{\frac{10368}{17}}$$

Rewrite the square root of the division \sqrt{\frac{10368}{17}} as the division of square roots \frac{\sqrt{10368}}{\sqrt{17}}.

$$\frac{\sqrt{10368}}{\sqrt{17}}$$

Factor 10368=72^{2}\times 2. Rewrite the square root of the product \sqrt{72^{2}\times 2} as the product of square roots \sqrt{72^{2}}\sqrt{2}. Take the square root of 72^{2}.

$$\frac{72\sqrt{2}}{\sqrt{17}}$$

Rationalize the denominator of \frac{72\sqrt{2}}{\sqrt{17}} by multiplying numerator and denominator by \sqrt{17}.

$$\frac{72\sqrt{2}\sqrt{17}}{\left(\sqrt{17}\right)^{2}}$$

The square of \sqrt{17} is 17.

$$\frac{72\sqrt{2}\sqrt{17}}{17}$$

To multiply \sqrt{2} and \sqrt{17}, multiply the numbers under the square root.

$$\frac{72\sqrt{34}}{17}$$