Question

Find the square roots of the following numbers by Division method:
1369

Answer 1

1369

$\begin{array}{cc}& 37\\ 3& \overline{13}\overline{69}\\ & -9\\ 67& 469\\ & -469\\ & 0\end{array}$
Steps:

Step(i)1369 is dividend. Pair it in groups of 2 digits i.e $\overline{13}\overline{69}$

Step(ii)Now for divisor,find the perfect square which is not greater than 13 which is $9\left(3^2\right)<13<16\left(4^2\right)$

Step (iii) Now take 3 as divisor and

$\begin{array}{cc}& 3\\ 3& \overline{13}\overline{69}\\ & -9\\ & 4\end{array}$

Step(iv) Now for new divisior double the old divisior and find a digit such that product of digit and the new divisor appended with that digit is the biggest number not greater than the new dividend and perform the division $(67\times 7=469)$

$\begin{array}{cc}67& 469\\ & -469\\ & 0\end{array}$

Hence, the square root of 1369 is 37.