Question

Find $\sqrt{3969}$ by the long division method

Answer 1

Step $1$ : We write $3969$ as $\overline{39}\overline{69}$ by grouping the digits into pairs, starting from right end.
Step $2$ : Find the number whose square is less than or equal to $39$. It is $6$.
Step $3$ : Put $6$ on the top and also write $6$ as a divisor.
Step $4$ : Multiply $6$ with $6$ and write the result $36$ under $39$ and subtract. The remainder is $3$.
Step $5$ : Bring down the pair $69$ by the side of this remainder $3$, yielding $369$.
Step $6$ : Double $6$, take the result $12$ and find the number ${}^{\prime }{n}^{\prime }$. Such that $12n\times n$ is just less than or equal to $369$.
Since $122\times 2=244;123\times 3=369,n=3$
Step $7$ : Write $123$ as the next divisor and put $3$ on the top along with $6$. Write the product $123\times 3=369$ under $369$ and subtract. Since the remainder is $0$, the division is complete.
Hence $\sqrt{3969}=63$.