Question

Find the square root of 1024 by division method?
(a) 42
(b) 48
(c) 38
(d) 32

Answer 1

Hint: In the above problem, we are asked to find the square root of 1024 by division method. For that, we are going to divide the number into two parts: the first part contains the first two numbers (1024) and the second part contains the last two numbers (1024). Then we will find a number by hit and trial whose square is lesser than or equal to the first two numbers (i.e. 10). Then we subtract the square of the number obtained from hit and trial from the first two numbers and write the remaining number. Remaining steps will be more clear in the below solution.

Complete step by step answer:
The number of which we have to find the square root by division method is:
1024
Now, we are going to divide the number into two parts in the following manner.
10 24
By hit and trial method, the number whose square is closest to 10 is 3. We know that the square of 3 is 9 which is less than 10. We cannot take 4 because its square is 16 and it is greater than 10.
\[3\left| \begin{align}
  & \underline{10}24 \\
 & \dfrac{-9}{01} \\
\end{align} \right|3\]
In the above division method, we have subtracted 9 from 10. Now, we are going to write the remaining number 24 after 1 and then the above division will look like:


\[3\left| \begin{align}
  & \underline{10}24 \\
 & \dfrac{-9\downarrow }{0124} \\
\end{align} \right|3\]
Now, we are going to multiply 3 by 2 and then write 6 below 3.
\[\begin{matrix}
   3 \\
   62 \\
\end{matrix}\left| \begin{align}
  & \underline{10}24 \\
 & \dfrac{-9\downarrow }{\begin{align}
  & 0124 \\
 & \dfrac{0124}{0000} \\
\end{align}} \\
\end{align} \right|32\]
In the above, by hit and trial method we have found the number 2 which we have multiplied by 62 and we have got 124 which on subtraction with 124 will get us the remainder 0. Also, we have written the number 2 after 3. So, the square root of 1024 is 32.
Hence, the correct option is (d).

Note:
 You can check the square root that you are getting above for 1024 is correct or not by multiplying 32 by itself.
Multiplying 32 by 32 we get,
\[\begin{align}
  & \text{ }32 \\
 & \dfrac{\times 32}{\begin{align}
  & \text{ }64 \\
 & \dfrac{96\times }{1024} \\
\end{align}} \\
\end{align}\]
As you can see that on multiplying 32 by 32 we are getting 1024 so the square root that we have found is correct.