Question

Find the square root of 130.

Answer 1

Hint: We first use the division of the square root process to find the square root of 130. We use the concept for both integer and decimal to find the value of \[\sqrt{130}\] till the 3-digit place after decimal.

Complete step by step solution:
We first have to find and check if the number 130 is a square number or not. 130 is not a square number and that’s why its square root can’t be broken into integers.
We take 2 digits as a set from the right end and complete the division. For decimal form we take the set from the right side of the decimal.
\[\begin{align}
  & 11 \\
 & 1\left| \!{\overline {\,
 \begin{align}
  & \overline{1}\overline{30}.\overline{00}\overline{00} \\
 & \underline{1} \\
 & 30 \\
\end{align} \,}} \right. \\
 & 21\left| \!{\overline {\,
 \begin{align}
  & \overline{30}.\overline{00}\overline{00} \\
 & \underline{21} \\
 & 900 \\
\end{align} \,}} \right. \\
\end{align}\]
Now we have to enter the decimal part. We keep doing the breaking in the set form till 3-digit place after decimal.
\[\begin{align}
  & 11.401 \\
 & 21\left| \!{\overline {\,
 \begin{align}
  & \overline{30}.\overline{00}\overline{00} \\
 & \underline{21} \\
 & 900 \\
\end{align} \,}} \right. \\
 & 224\left| \!{\overline {\,
 \begin{align}
  & 900\overline{00} \\
 & \underline{896} \\
 & 400 \\
\end{align} \,}} \right. \\
 & 22801\left| \!{\overline {\,
 \begin{align}
  & 40000 \\
 & \underline{22801} \\
 & 17199 \\
\end{align} \,}} \right. \\
\end{align}\]
Therefore, the value of $ \sqrt{130} $ is $ 11.401 $ .
So, the correct answer is “ $ 11.401 $ ”.

Note: The long-division method and arranging the set of 2 digits is different for integer and decimal. But taking double for the next division and putting a particular number is the same process for both of them. Since 130 is a non-perfect square number, we will find the value of root 130 using the long division method as shown above.