Solve sqrt{1-(1/4)^2}

$$\sqrt { 1 - ( \frac { 1 } { 4 } ) ^ { 2 } }$$

Evaluate

$$\frac{\sqrt{15}}{4}\approx 0.968245837$$

Solution Steps

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\sqrt{1-\frac{1}{16}}$$

Convert 1 to fraction \frac{16}{16}.

$$\sqrt{\frac{16}{16}-\frac{1}{16}}$$

Since \frac{16}{16} and \frac{1}{16} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{16-1}{16}}$$

Subtract 1 from 16 to get 15.

$$\sqrt{\frac{15}{16}}$$

Rewrite the square root of the division \sqrt{\frac{15}{16}} as the division of square roots \frac{\sqrt{15}}{\sqrt{16}}.

$$\frac{\sqrt{15}}{\sqrt{16}}$$

Calculate the square root of 16 and get 4.

$$\frac{\sqrt{15}}{4}$$