Solve 1/2/sqrt{1-{left(frac{1{2}right)}^2}}

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

Evaluate

$$\frac{\sqrt{3}}{3}\approx 0.577350269$$

Solution Steps

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

$$\frac{\frac{1}{2}}{\sqrt{1-\frac{1}{4}}}$$

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

$$\frac{\frac{1}{2}}{\sqrt{\frac{4}{4}-\frac{1}{4}}}$$

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

$$\frac{\frac{1}{2}}{\sqrt{\frac{4-1}{4}}}$$

Subtract 1 from 4 to get 3.

$$\frac{\frac{1}{2}}{\sqrt{\frac{3}{4}}}$$

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

$$\frac{\frac{1}{2}}{\frac{\sqrt{3}}{\sqrt{4}}}$$

Calculate the square root of 4 and get 2.

$$\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}$$

Divide \frac{1}{2} by \frac{\sqrt{3}}{2} by multiplying \frac{1}{2} by the reciprocal of \frac{\sqrt{3}}{2}.

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

Rationalize the denominator of \frac{2}{2\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{2\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

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

Cancel out 2 in both numerator and denominator.

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