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

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

Evaluate

$$1$$

Solution Steps

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

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

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

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

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

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

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

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

The square of \sqrt{3} is 3.

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

Add 1 and 3 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

$$1$$