Question

Find the square root of $484$ using long division method.

Answer 1

Let's find the square root of $484$ using long division method:

Step 1:
Place a bar over the pair of numbers starting from the unit place or right-hand side of the number.
$\overline{4}\overline{84}.$

Step 2:
Take the largest number as the divisor whose square is less than or equal to the number on the extreme left of the number $\left(4\right).$ The digit on the extreme left is the dividend. Divide and write the quotient. Here the quotient is $2$ and the remainder is $0.$


Step 3:
Next, we bring down the number, which is under the bar, to the right side of the remainder. Here, we bring down $84.$ Now, $84$ is our new dividend.


Step 4:
Now, double the value of the existing quotient, and enter it with a blank space on its right.


Step 5:
Next, we have to select the largest digit for the unit place of the divisor $(4-)$ such that the current divisor, when multiplied by the new digit at its unit’s place, is equal to or less than the current dividend $\left(84\right).$
In this case, $4\underset{–}{2}\times \underset{–}{2}=84.$ So, the new unit place's digit is $2.$

Step 6:
Finally, the remainder is $0,$ and we have no number left for division. Therefore, the square root of $484$ is the final quotient, i.e., $\underset{–}{\sqrt{484}=22}.$