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

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

Evaluate

$$\frac{\sqrt{3}}{2}\approx 0.866025404$$

Solution Steps

Calculate 1 to the power of 2 and get 1.

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

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

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

Convert 1 to fraction \frac{4}{4}.

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

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

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

Subtract 1 from 4 to get 3.

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

Rewrite the square root of the division \sqrt{\frac{3}{4}} as the division of square roots \frac{\sqrt{3}}{\sqrt{4}}.

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

Calculate the square root of 4 and get 2.

$$\frac{\sqrt{3}}{2}$$