Evaluate (2 1/2)^2

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

Convert $2 \frac{1}{2}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

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

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

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $2$ .

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

Add $4$ and $1$ .

${(\frac{5}{2})}^{2}$

Apply the product rule to $\frac{5}{2}$ .

$\frac{5^{2}}{2^{2}}$

Raise $5$ to the power of $2$ .

$\frac{25}{2^{2}}$

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

$\frac{25}{4}$

The result can be shown in multiple forms.

Exact Form:

$\frac{25}{4}$

Decimal Form:

$6.25$

Mixed Number Form:

$6 \frac{1}{4}$