Question

Find the square root of 9801 by long division method.

Answer 1

Hint: For solving this question you should know about the long division method. In this problem we will divide 9801 and will get the answer by solving this division with a long division method. First, we will solve using that division and then the quotient will be our answer.

Complete step-by-step solution:
According to the question we have to find the square root of 9801 by long division method. As we know for solving the long division method, we use just few simple steps as:
Step 1: Divide our given term by which it is asked and it will be a simple division.
Step 2: Now we will multiply the quotient with the divisor and put the value of that as subtraction of the first digit.
Step 3: Then we put the remaining single digit with the result of the subtraction and then we get it as a new number.
Step 4: Now we get a new number. We will then apply the same above steps to it and finally get the last remainder that can’t be further divisible by any number or we get a remainder.
Step 5: If you want to check the answer, then you can do it with the formula: Dividend = Divisor $\times $ Quotient + Remainder.
Now if we see our question, then our dividend is 9801, so we can write it as,
$\begin{align}
  \text{ 99} & \\
  \text{ 9}\left| \!{\overline {\,
 \begin{align}
  & 9801 \\
 & 81 \\
\end{align} \,}} \right. & \\
  \text{189}\left| \!{\overline {\,
 \begin{align}
  & 1701 \\
 & 1701 \\
\end{align} \,}} \right. & \\
  \text{ }\left| \!{\overline {\,
 0000 \,}} \right. & \\
\end{align}$
So, it is clear that the quotient is 99 and the square root of 9801 is 99.

Note: While solving this question or all other related questions to the long division method, always try to make it fully divisible as the remainder remains zero. And if the question is asking for the square root, then it is mandatory that the remainder is zero. If it is not so, then your calculations are 100% wrong and the solution will never be correct.