Solve sqrt{(frac{sqrt{3}}{2})^2+(1/2)^2}

$$\sqrt { ( \frac { \sqrt { 3 } } { 2 } ) ^ { 2 } + ( \frac { 1 } { 2 } ) ^ { 2 } }$$

Evaluate

$$1$$

Solution Steps

To raise \frac{\sqrt{3}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\sqrt{\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}+\left(\frac{1}{2}\right)^{2}}$$

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

$$\sqrt{\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}+\frac{1}{4}}$$

To add or subtract expressions, expand them to make their denominators the same. Expand 2^{2}.

$$\sqrt{\frac{\left(\sqrt{3}\right)^{2}}{4}+\frac{1}{4}}$$

Since \frac{\left(\sqrt{3}\right)^{2}}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{\left(\sqrt{3}\right)^{2}+1}{4}}$$

The square of \sqrt{3} is 3.

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

Add 3 and 1 to get 4.

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

Divide 4 by 4 to get 1.

$$\sqrt{1}$$

Calculate the square root of 1 and get 1.

$$1$$

Factor

$$1$$