Question

Question 1 (iii)
Find the square roots of each of the following numbers by Division method:

3481

Answer 1

3481

$\begin{array}{cc}& 59\\ 5& \overline{34}\overline{81}\\ & -25\\ 109& 981\\ & -981\\ & 0\end{array}$
Steps
Step(i)3481 is dividend. Pair it in groups of 2 digits i.e $\overline{34}\overline{81}$
Step(ii)Now for divisor,find the perfect square which is not greater than 44 which is $25\left(5^2\right)<34<36\left(6^2\right)$
Step (iii)andNow take 6 as divisor and
$\begin{array}{cc}& 5\\ 5& \overline{34}\overline{81}\\ & -25\\ 109& 9\end{array}$
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 $(109\times 9=981$)
$\begin{array}{cc}109& 981\\ & -981\\ & 0\end{array}$

Hence, the square root of 3481 is 59.