Square root through prime factorisation — lesson. Mathematics CBSE, Class 8.

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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.

$\begin{array}{l} \underline{2 | 324} \\ \underline{2 | 162} \\ \underline{3 | 81} \\ \underline{3 | 27} \\ \underline{3 | 9} \\ \underline{3 | 3} \\ | 1 \end{array}$

$324 = 2 \times 2 \times 3 \times 3 \times 3 \times 3$

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.

$\sqrt{324}$

$=$

$2 \times 3 \times 3$

$\sqrt{324}$

$=$

$18$