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

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

Simplify each term.

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

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

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

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

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

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

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

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

$\frac{1}{2} + \frac{2^{\frac{1}{2} \cdot 2}}{2^{2}}$

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

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

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

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

$\frac{1}{2} + \frac{2 \cdot 1}{2 \cdot 2}$

Cancel the common factor.

$\frac{1}{2} + \frac{2 \cdot 1}{2 \cdot 2}$

Rewrite the expression.

$\frac{1}{2} + \frac{1}{2}$

Combine fractions.

Combine the numerators over the common denominator.

$\frac{1 + 1}{2}$

Simplify the expression.

Add $1$ and $1$ .

$\frac{2}{2}$

Divide $2$ by $2$ .

$1$

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

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