Evaluate (1 1/2)^2

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

Step 1

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

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

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

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

Write $1$ as a fraction with a common denominator.

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

Combine the numerators over the common denominator.

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

Add $2$ and $1$ .

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

Step 2

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

$\frac{3^{2}}{2^{2}}$

Step 3

Raise $3$ to the power of $2$ .

$\frac{9}{2^{2}}$

Step 4

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

$\frac{9}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{4}$

Decimal Form:

$2.25$

Mixed Number Form:

$2 \frac{1}{4}$