Solve sqrt{5^2-(25/13)^2}

$$\sqrt { 5 ^ { 2 } - ( \frac { 25 } { 13 } ) ^ { 2 } }$$

Evaluate

$$\frac{60}{13}\approx 4.615384615$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

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

Calculate \frac{25}{13} to the power of 2 and get \frac{625}{169}.

$$\sqrt{25-\frac{625}{169}}$$

Convert 25 to fraction \frac{4225}{169}.

$$\sqrt{\frac{4225}{169}-\frac{625}{169}}$$

Since \frac{4225}{169} and \frac{625}{169} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{4225-625}{169}}$$

Subtract 625 from 4225 to get 3600.

$$\sqrt{\frac{3600}{169}}$$

Rewrite the square root of the division \frac{3600}{169} as the division of square roots \frac{\sqrt{3600}}{\sqrt{169}}. Take the square root of both numerator and denominator.

$$\frac{60}{13}$$

Factor

$$\frac{2 ^ {2} \cdot 3 \cdot 5}{13} = 4\frac{8}{13} = 4.615384615384615$$