Solve sqrt{13^2-{left(50/13right)}^2}

$$\sqrt{ { 13 }^{ 2 } - { \left( \frac{ 50 }{ 13 } \right) }^{ 2 } }$$

Evaluate

$$\frac{\sqrt{26061}}{13}\approx 12.418015163$$

Solution Steps

Calculate 13 to the power of 2 and get 169.

$$\sqrt{169-\left(\frac{50}{13}\right)^{2}}$$

Calculate \frac{50}{13} to the power of 2 and get \frac{2500}{169}.

$$\sqrt{169-\frac{2500}{169}}$$

Convert 169 to fraction \frac{28561}{169}.

$$\sqrt{\frac{28561}{169}-\frac{2500}{169}}$$

Since \frac{28561}{169} and \frac{2500}{169} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{28561-2500}{169}}$$

Subtract 2500 from 28561 to get 26061.

$$\sqrt{\frac{26061}{169}}$$

Rewrite the square root of the division \sqrt{\frac{26061}{169}} as the division of square roots \frac{\sqrt{26061}}{\sqrt{169}}.

$$\frac{\sqrt{26061}}{\sqrt{169}}$$

Calculate the square root of 169 and get 13.

$$\frac{\sqrt{26061}}{13}$$