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Steps to find the square root of a number:
Step 1: Write the given natural number as a product of prime factors.
Step 2: Group the factors in pairs so that both factors in each pair are equal.
Step 3: Now, see whether some factors are leftover or not. If no factor is leftover in grouping, then the given number is a perfect square. Otherwise, it is not a perfect square.
Step 4: Take one factor from each group and multiply them to obtain the number whose square is the given number.
Let's see an example to understand this concept clear.
Example:
Find \(\sqrt{324}\).
We need to find the value of \(\sqrt{324}\).
Step 1: Write \(324\) as a product of prime factors.
\(324 = 2 \times 2 \times 3 \times 3 \times 3 \times 3\)
Step 2: Group the prime factors.
\(324 = (2 \times 2) \times (3 \times 3) \times (3 \times 3)\)
Step 3: Here, no factor is leftover in grouping.
So, the given number is a perfect square.
Step 4: Now, take one factor commonly from each group.
\(\sqrt{324}\) \(=\) \(2 \times 3 \times 3\)
\(\sqrt{324}\) \(=\) \(18\)
Therefore, the square root of \(\sqrt{324}\) is \(18\).
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