Calculate the Square Root of 272¼: Mixed Number Evaluation

To solve for the square root of $272\frac{1}{4}$, we can follow these steps:

• Step 1: Convert the mixed number to an improper fraction. $272\frac{1}{4}$ becomes $\frac{1089}{4}$.
• Step 2: Find the square root of $\frac{1089}{4}$.

Step 1: Convert the mixed number to an improper fraction:
To convert $272\frac{1}{4}$ to an improper fraction:

• Multiply the whole number 272 by 4: $272 \times 4 = 1088$
• Add the numerator of the fraction: $1088 + 1 = 1089$
• Thus, $272\frac{1}{4}$ is $\frac{1089}{4}$.

Step 2: Calculate the square root of $\frac{1089}{4}$:
The square root of a fraction $\frac{a}{b}$ is $\frac{\sqrt{a}}{\sqrt{b}}$.

• $\sqrt{\frac{1089}{4}} = \frac{\sqrt{1089}}{\sqrt{4}}$
• The square root of 1089 is 33, since $33 \times 33 = 1089$.
• The square root of 4 is 2, since $2 \times 2 = 4$.

Therefore, $\sqrt{\frac{1089}{4}} = \frac{33}{2} = 16.5 = 16\frac{1}{2}$.

Thus, the square root of $272\frac{1}{4}$ is $16\frac{1}{2}$.