Solve sqrt{5^2-(6/13/13)^2}

$$\sqrt { 5 ^ { 2 } - ( \frac { 6 / 13 } { 13 } ) ^ { 2 } }$$

Evaluate

$$\frac{\sqrt{713989}}{169}\approx 4.999873952$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\sqrt{25-\left(\frac{\frac{6}{13}}{13}\right)^{2}}$$

Express \frac{\frac{6}{13}}{13} as a single fraction.

$$\sqrt{25-\left(\frac{6}{13\times 13}\right)^{2}}$$

Multiply 13 and 13 to get 169.

$$\sqrt{25-\left(\frac{6}{169}\right)^{2}}$$

Calculate \frac{6}{169} to the power of 2 and get \frac{36}{28561}.

$$\sqrt{25-\frac{36}{28561}}$$

Subtract \frac{36}{28561} from 25 to get \frac{713989}{28561}.

$$\sqrt{\frac{713989}{28561}}$$

Rewrite the square root of the division \sqrt{\frac{713989}{28561}} as the division of square roots \frac{\sqrt{713989}}{\sqrt{28561}}.

$$\frac{\sqrt{713989}}{\sqrt{28561}}$$

Calculate the square root of 28561 and get 169.

$$\frac{\sqrt{713989}}{169}$$