### Theory:

The repeated subtraction method is one of the simplest way to find the square root of a number.
We know that the square number can be written as the sum of consecutive odd numbers starting from $$1$$.

We can obtain the square root of a number by repeatedly subtracting the successive odd numbers (starting from $$1$$) from the given square number till we reach zero.

At one particular step, we get zero. The step where we get zero is the square root of a given number.
If we did not get zero, the given number is not a perfect square.

Let's see an example to understand this concept.
Example:
Obtain the square root of $$49$$ by repeated subtraction method.

Solution:

The given number is $$49$$.

We need to find the square root of $$49$$ by the repeated subtraction method.

Subtract the given number by the odd numbers starting from $$1$$ till we get $$0$$.

Step 1: $$49 - 1 = 48$$

Step 2: $$48 - 3 = 45$$

Step 3: $$45 - 5 = 40$$

Step 4: $$40 - 7 = 33$$

Step 5: $$33 - 9 = 24$$

Step 6: $$24 - 11 = 13$$

Step 7:  $$13 - 13 = 0$$

Here we get zero on the $$7^{\text{th}}$$ step. That is $$\sqrt{49} = 7$$.

Therefore, the square root of $$49$$ is $$7$$.
Can we find a square root of $$15876$$ by repeated subtraction method?

Yes, we can, but if we use this method for a large number like $$15876$$, we can find the square root, but it will take a huge time. So, we use this method only for small numbers.

We will use some other methods, like prime factorization and long division, to find the given number's square root.