If (1101)² = 1212201, find the value of √ 121.2201.

The correct option is 11.01.

Let us understand the step-by-step derivation to find the value of $\sqrt{121.2201}$ based on the given information.

We are given the relationship:
${\left(1101\right)}^2=1212201$
This equation implies that the square root of 1212201 is:
$\sqrt{1212201}=1101$

Now, we want to find the square root of the decimal number 121.2201.
We can express the decimal number as a fraction:
$121.2201=\frac{1212201}{10000}$

Taking the square root on both sides:
$\sqrt{121.2201}=\sqrt{\frac{1212201}{10000}}$
Using the property of square roots, $\sqrt{\frac{a}{b}}=\frac{\sqrt{a\sqrt{}}}{\sqrt{b}}$, we write:
$\sqrt{121.2201}=\frac{\sqrt{1212201}}{\sqrt{10000}}$

We know that $\sqrt{1212201}=1101$ and $\sqrt{10000}=100$ (since ${100}^2=10000$).
Substituting these values into the fraction:
$\sqrt{121.2201}=\frac{1101}{100}$
Converting the fraction back to a decimal by moving the decimal point two places to the left:
$\sqrt{121.2201}=11.01$

Therefore, the value of $\sqrt{121.2201}$ is 11.01, which corresponds to the second option.