Question

How to find the square root of $119$ ?

Answer 1

Calculate the square root of $119$ using long division method

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.
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 that $2\mathrm{xy}\times \mathrm{y}$ is less than or equal to the result of the concatenation.
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 divisor $<$ dividend.

Hence, the square root of $119$ is $10.908$.