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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.
\(144 = 2 \times 2 \times 2 \times 2 \times 3 \times 3\)
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 \(1.44\) \(=\) \(1.2\).
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