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

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

Evaluate

$$\frac{\sqrt{2}}{2}\approx 0.707106781$$

Solution Steps

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

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

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

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

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

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

Add 1 and 1 to get 2.

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

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

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

Calculate the square root of 1 and get 1.

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

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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