Question

While finding the square root of 121 by repeated subtraction, in which step does 85 occur?

Answer 1

The sum of first $n$ odd natural numbers is $n^2$. This fact is used to find the square root of a number by repeated subtraction. In finding the square root of 121 by repeated subtraction the steps involved are:-
$\begin{array}{cc}StepNumber& Value\\ 1& 121-1=120\\ 2& 120-3=117\\ 3& 117-5=112\\ 4& 112-7=105\\ 5& 105-9=96\\ 6& 96-11=85\\ 7& 85-13=72\\ 8& 72-15=57\\ 9& 57-17=40\\ 10& 40-19=21\\ 11& 21-21=0\end{array}$
You can clearly see that 85 occurs in the 6${}^{th}$ step.