Question

While finding the square root of 81 by repeated subtraction, in which step does 17 occur?

• A. 3${}^{rd}$
• B. 5${}^{th}$
• C. 8${}^{th}$
• D. 6${}^{th}$

Answer 1

The correct option is C 8${}^{th}$

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 81 by repeated subtraction the steps involved are:-
$\begin{array}{cc}StepNumber& Value\\ 1& 81-1=80\\ 2& 80-3=77\\ 3& 77-5=72\\ 4& 72-7=65\\ 5& 65-9=56\\ 6& 56-11=45\\ 7& 45-13=32\\ 8& 32-15=17\\ 9& 17-17=0\end{array}$
You can clearly see that 17 occurs in the 8${}^{th}$ step.