Question

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

529

Answer 1

529

$\begin{array}{cc}& 23\\ 2& \overline{5}\overline{29}\\ & -4\\ 43& 129\\ & -129\\ & 0\end{array}$

Steps:

Step(i) 529 is dividend. Pair it in groups of 2 digits i.e $\overline{5}\overline{29}$

Step(ii) Now for divisor, find the perfect square which is not greater than 44 which is $4\left(2^2\right)<5<9\left(3^2\right)$

Step (iii) Now take 2 as divisor and

$\begin{array}{cc}& 2\\ 2& \overline{5}\overline{29}\\ & -4\\ & 1\end{array}$

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 $(43\times 3=129$)

$\begin{array}{cc}43& 129\\ & -129\\ & 0\end{array}$

Hence, the square root of 529 is 23.