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

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

Evaluate

$$\frac{\sqrt{3}}{4}\approx 0.433012702$$

Solution Steps

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

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

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

$$\sqrt{\frac{1}{4}-\frac{1}{16}}$$

Least common multiple of 4 and 16 is 16. Convert \frac{1}{4} and \frac{1}{16} to fractions with denominator 16.

$$\sqrt{\frac{4}{16}-\frac{1}{16}}$$

Since \frac{4}{16} and \frac{1}{16} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{4-1}{16}}$$

Subtract 1 from 4 to get 3.

$$\sqrt{\frac{3}{16}}$$

Rewrite the square root of the division \sqrt{\frac{3}{16}} as the division of square roots \frac{\sqrt{3}}{\sqrt{16}}.

$$\frac{\sqrt{3}}{\sqrt{16}}$$

Calculate the square root of 16 and get 4.

$$\frac{\sqrt{3}}{4}$$