Question

How to find the square root of $10201$ by long division method ?

Answer 1

Long division method to find the square root of $10201$.

1. Break the given number into pairs from right to left. If the last digit is alone or unpaired then add $0$ before it.
2. Choose a number $\mathrm{x}$ such that ${\mathrm{x}}^2\le$first-pair. Here $\mathrm{x}=1$.
3. Calculate $2\mathrm{x}$ and copy the next pair and concatenate with the remainder of the previous part.
4. Now, concatenate $y$ to $2\mathrm{x}$ such $2\mathrm{xy}\times \mathrm{y}$ is less than or equal to the result of the concatenation. Here $\mathrm{y}=0$.
5. Go to step 2 and repeat till the remainder is zero or divisor $>$ dividend.

As observed in the figure the process is terminated when the remainder becomes $0$.

Therefore, the square root of $10201$ is $101$.