Solve sqrt{(8/13)^2-(2/13)^2}

$$\sqrt { ( \frac { 8 } { 13 } ) ^ { 2 } - ( \frac { 2 } { 13 } ) ^ { 2 } }$$

Evaluate

$$\frac{2\sqrt{15}}{13}\approx 0.595843592$$

Solution Steps

Calculate \frac{8}{13} to the power of 2 and get \frac{64}{169}.

$$\sqrt{\frac{64}{169}-\left(\frac{2}{13}\right)^{2}}$$

Calculate \frac{2}{13} to the power of 2 and get \frac{4}{169}.

$$\sqrt{\frac{64}{169}-\frac{4}{169}}$$

Since \frac{64}{169} and \frac{4}{169} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{64-4}{169}}$$

Subtract 4 from 64 to get 60.

$$\sqrt{\frac{60}{169}}$$

Rewrite the square root of the division \sqrt{\frac{60}{169}} as the division of square roots \frac{\sqrt{60}}{\sqrt{169}}.

$$\frac{\sqrt{60}}{\sqrt{169}}$$

Factor 60=2^{2}\times 15. Rewrite the square root of the product \sqrt{2^{2}\times 15} as the product of square roots \sqrt{2^{2}}\sqrt{15}. Take the square root of 2^{2}.

$$\frac{2\sqrt{15}}{\sqrt{169}}$$

Calculate the square root of 169 and get 13.

$$\frac{2\sqrt{15}}{13}$$