Solution:We are asked to find the value of by using the long division method.
We know that the steps involved in this process are
(1) We divide the number into pairs of 2 digits starting from the right side.
(2) We take the square less than and near to the first pair on the left and take the square root of that near number as the first digit of the required value. Let us assume it as ′x′
(3) We subtract the first pair and the near square to that pair and take the second pair as a set of numbers.
(4) If the new set of number is ′n′ then we double the first digit we got in the step (2) to make the problem as
2xk×k ≤ n
Here 2xk is a number but not 2x×k
Here, the value of ′k′ will be the second digit of the required square root.
Let us take the number 784 as the pairs of 2 numbers starting from right then we get
Here we can see that the pairs are 7, 84
Now let us take the perfect square less than and near to 7 that is 4
By taking the square root of 4 that is 2 as first digit of required square root then we get
Now, by subtracting number 7 and 4 and taking the second pair 84 then we get
Now, let us double the number 2 to form the equation as
4k × k ≤ 384
Here, we know that ′k′ is a digit.
By, using the trial and error method we get
By using this condition we get
Here, we can see that we got 0 so that we can stop the process.
Therefore we can conclude that the square root of 784 is 28.