If `(1101)^(2)` = 1212201, find the value of `sqrt(121.2201)`.

Options

A. 110.1
B. 11.01
C. 1.101
D. 11.001

Answer

To solve the problem, we need to find the value of \( \sqrt{121.2201} \) given that \( (1101)^2 = 1212201 \).

### Step-by-Step Solution:

1. **Understanding the Given Information**:
We know that \( (1101)^2 = 1212201 \). This means that \( 1101 \) is the square root of \( 1212201 \).

2. **Relating the Square Root to the Decimal**:
We need to find \( \sqrt{121.2201} \). Notice that \( 121.2201 \) can be expressed as \( \frac{1212201}{10000} \) because moving the decimal point two places to the left is equivalent to dividing by \( 10000 \).

3. **Applying the Square Root Property**:
Using the property of square roots, we have:
\[ \sqrt{121.2201} = \sqrt{\frac{1212201}{10000}} = \frac{\sqrt{1212201}}{\sqrt{10000}} \]

4. **Calculating the Square Roots**:
We already know \( \sqrt{1212201} = 1101 \) (from the given information).
We also know that \( \sqrt{10000} = 100 \).

5. **Final Calculation**:
Now substituting the values we found:
\[ \sqrt{121.2201} = \frac{1101}{100} = 11.01 \]

Thus, the value of \( \sqrt{121.2201} \) is \( 11.01 \).