Solve sqrt{1-(9/46)^2}

$$\sqrt { 1 - ( \frac { 9 } { 46 } ) ^ { 2 } }$$

Evaluate

$$\frac{\sqrt{2035}}{46}\approx 0.980673354$$

Solution Steps

Calculate \frac{9}{46} to the power of 2 and get \frac{81}{2116}.

$$\sqrt{1-\frac{81}{2116}}$$

Convert 1 to fraction \frac{2116}{2116}.

$$\sqrt{\frac{2116}{2116}-\frac{81}{2116}}$$

Since \frac{2116}{2116} and \frac{81}{2116} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{2116-81}{2116}}$$

Subtract 81 from 2116 to get 2035.

$$\sqrt{\frac{2035}{2116}}$$

Rewrite the square root of the division \sqrt{\frac{2035}{2116}} as the division of square roots \frac{\sqrt{2035}}{\sqrt{2116}}.

$$\frac{\sqrt{2035}}{\sqrt{2116}}$$

Calculate the square root of 2116 and get 46.

$$\frac{\sqrt{2035}}{46}$$