Evaluate (( square root of 3)/2)^2+(1/2)^2

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

Simplify each term.

Apply the product rule to $\frac{\sqrt{3}}{2}$ .

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

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

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

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Combine $\frac{1}{2}$ and $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Raise $2$ to the power of $2$ .

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

Apply the product rule to $\frac{1}{2}$ .

$\frac{3}{4} + \frac{1^{2}}{2^{2}}$

One to any power is one.

$\frac{3}{4} + \frac{1}{2^{2}}$

Raise $2$ to the power of $2$ .

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

Combine fractions.

Combine the numerators over the common denominator.

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

Simplify the expression.

Add $3$ and $1$ .

$\frac{4}{4}$

Divide $4$ by $4$ .

$1$