Question

Find the square root of 17 by using the long division method.

Answer 1

Hint: since we have to find the square root by long division method as per the long division method, we have to Take the first digit of the dividend. Then divide it by the divisor and write the answer on top as the quotient. After that Subtract the result from the digit and write the difference below. Then Bring down the next number (if present). Repeat the same process. Let us find the root one-digit decimal accuracy.

Complete step by step answer:
Step 1: Write \[17\] as shown below. Start grouping the number in pairs from the right end. For \[17\], both the numbers will be grouped under one bar.
\[\overline {17} \]
Step 2:
Find the largest number, which, when multiplied with itself, will give\[17\]or a smaller number closest to \[17\]. so \[4\] is the required number.
\[\begin{align}
  & \;\;\;\;\;\;4 \\
 & 4\left| \!{\overline {\,
 \begin{align}
  & 17.00 \\
 & 16 \\
\end{align} \,}} \right.
\end{align}\]
Step 3: We get the remainder as 1 in this step. Now, place 2 pairs of zeros after the decimal point and continue the long division. Bring one pair of zeros down. Add the quotient 4 to the divisor, which is also 4. Thus, 8 will be placed as the new divisor on the tens place, with a blank on one's place. This blank will be filled by a number which when multiplied with the quotient, will give the result 100 or a smaller number closest to 100. Here, ( \[81 \times 1 = 81\]) is the closest to 100. So, 1 will be placed on the blank place just next to the number 4.
\[\begin{align}
  & \;\;\;\;\;\;4.1 \\
 & 4\left| \!{\overline {\,
 \begin{align}
  & 17.00 \\
 & 16 \\
& \overline{100}\\
& 81\\
\end{align} \,}} \right.
\end{align}\]
That's it! The answer is on top. The square root of \[17\] with one-digit decimal accuracy is \[4.1\]. we can notice that We can add decimals by simply adding more sets of \[00\]and repeating the last two steps .

Note: In math, long division is a method used for dividing large numbers into groups or parts. Long division helps in breaking the division problem into a sequence of easier steps. Just like all division problems, a large number, which is the dividend, is divided by another number, which is called the divisor, to give a result called the quotient and sometimes a remainder.