### Theory:

We can follow the below steps to find out the square root of the decimal numbers.
Step 1: Calculate the square root of the given decimal number without the decimal.

Step 2: Put the decimal point in the obtained number such that it is half that of the original number.

Note:

(i) If the original number contains a double decimal, then the square of that number will be a single decimal.

$$\frac{\text{Number of decimals in the original number}}{2} = \frac{2}{2} = 1$$

(ii) If the original number contains four decimal, then the square of that number will have two decimal.

$$\frac{\text{Number of decimals in the original number}}{2} = \frac{4}{2} = 2$$
Let's see an example to understand this concept clear.
Example:
Calculate the square root of $$1.44$$.

Solution:

The given number is $$1.44$$.

First, calculate the square root of the given decimal number without the decimal.

We have to write $$144$$ as a product of prime factors.

$\begin{array}{l}\underset{¯}{2|144}\\ \underset{¯}{2|72\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}}\\ \underset{¯}{2|36\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}}\\ \underset{¯}{2|18\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}}\\ \underset{¯}{3|9\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}}\\ \underset{¯}{3|3\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}}\\ \phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}|1\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\end{array}$

$$144 = 2 \times 2 \times 2 \times 2 \times 3 \times 3$$

Now, group the prime factors.

$$144 = (2 \times 2) \times (2 \times 2) \times (3 \times 3)$$

Here, no factor is leftover in grouping.

Therefore, the given number is a perfect square.

Now, take one factor commonly from each group.

$$=$$ $$2 \times 2 \times 3$$

$$=$$ $$12$$

Thus, $$\sqrt{144} = 12$$.

Now, put the decimal point in the obtained number such that it is half that of the original number.

The given number has a double decimal so that the answer would be a single decimal.

That is $$1.2$$.

Therefore, the square root of a given decimal number is $$1.44$$ $$=$$ $$1.2$$.