Question

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

5776

Answer 1

5776

$\begin{array}{cc}& 76\\ 7& \overline{57}\overline{76}\\ & -49\\ 146& 876\\ & -876\\ & 0\end{array}$
Steps
Step(i)5776 is dividend. Pair it in groups of 2 digits i.e $\overline{57}\overline{76}$
Step(ii)Now for divisor,find the perfect square which is not greater than 44 which is $49\left(7^2\right)<57<64\left(8^2\right)$
Step (iii)andNow take 7 as divisor and
$\begin{array}{cc}& 7\\ 7& \overline{57}\overline{76}\\ & -49\\ & 8\end{array}$
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 $(146\times 6=876$)
$\begin{array}{cc}146& 876\\ & -876\\ & 0\end{array}$

Hence, the square root of 5776 is 76.