Question

How do you find the square root of 6889?

Answer 1

Hint: We will write the given number as a group of paired digits. Then we will use the long division method to find the square root of the number. We will consider the first pair of digits of the number and subtract from it the largest square which is less than the number formed by the first pair of digits. This is the first step of the long division method. Continuing with the next steps, we will obtain the square root.

Complete step by step answer:
We define the square root of a number to be the value such that when it is multiplied to itself, it gives the product as the given number. So, we have to find a number such that after multiplying it to itself, we get the number 6889.
Let us look at the long division process while computing the square root of 6889. The first step is to consider the first pair of digits from 6889 which is 68. We will subtract the largest square which is less than 68 from it. So, we have
 $ \begin{matrix}
   {} & 8 & {} & {} & {} \\
   8 & 6 & 8 & 8 & 9 \\
   - & 6 & 4 & \downarrow & \downarrow \\
   {} & 0 & 4 & 8 & 9 \\
\end{matrix} $
Now, we will double the quotient for the next step and add one more digit in the units place to it so that this new number multiplied to the digit in the units place to get the highest number which is less than the remainder. We will choose the digit 3, so we have $ 163\times 3=489 $ . Representing this in the long division format, we get the following,
 $ \begin{matrix}
   {} & 8 & 3 & {} & {} \\
   8 & 6 & 8 & 8 & 9 \\
   - & 6 & 4 & \downarrow & \downarrow \\
   163 & 0 & 4 & 8 & 9 \\
   - & {} & 4 & 8 & 9 \\
   {} & {} & {} & {} & 0 \\
\end{matrix} $
Hence, the square root of 6889 is 83.

Note:
The long division method to find the square root of a given number is very useful in finding the square root for large numbers. Factorization is another method for finding the square root of a given number. But for large numbers, it may become very cumbersome. We should do the calculations explicitly so that we can avoid making any errors and obtain the correct answer.