Solve -sqrt{1-(2/13)^2}

$$- \sqrt { 1 - ( \frac { 2 } { 13 } ) ^ { 2 } }$$

Evaluate

$$-\frac{\sqrt{165}}{13}\approx -0.988094814$$

Solution Steps

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

$$-\sqrt{1-\frac{4}{169}}$$

Convert 1 to fraction \frac{169}{169}.

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

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

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

Subtract 4 from 169 to get 165.

$$-\sqrt{\frac{165}{169}}$$

Rewrite the square root of the division \sqrt{\frac{165}{169}} as the division of square roots \frac{\sqrt{165}}{\sqrt{169}}.

$$-\frac{\sqrt{165}}{\sqrt{169}}$$

Calculate the square root of 169 and get 13.

$$-\frac{\sqrt{165}}{13}$$