Question

Find the square root of 529 using the long division method.

Answer 1

Hint: First of all divide the digits into pairs of two starting from the rightmost digit to carry out the long division method. Then select the largest number as a division whose square is less than or equal to the number on the extreme left. Repeat these steps after doubling the division each time to get the desired result.

Complete step-by-step answer:
Here, we have to find a square of 529 which is \[\sqrt{529}\] by long division method.
1. First of all, we have to group the digits of numbers in pairs, starting with digits in the units place. For this, we will place a bar over the pair of digits starting from the unit’s digit. In case of an odd number of digits, the left-most digit will also have a bar as shown below.
\[\overline{5}\text{ }\overline{29}\]
2. Now, we will take the largest number as the divisor whose square is less than or equal to the number on the extreme left that is 5. So, 5 is our dividend. Divide and write the quotient. Here, we will get the quotient as 2 and remainder as 1. We will do it as follows:

3. We then bring down the digits which are under the next bar to the right side of the remainder. In this case, we bring down 29. Now 129 is our new dividend. We will do it as follows.
 

4. Now double the value of quotient and enter it with a blank on the right side. We will do it as follows:

5. Now we have to select the largest digit for the unit place of the divisor (4 ___ ) such that the new number, when multiplied by the new digit at the unit’s place is equal to or less than the dividend (129).
In this case, 43 x 3 = 129. So our new digit is 3. We will do it as follows:

6. Now our remainder is 0 and we have no number left for multiplication. Therefore, we get \[\sqrt{529}=23\]
Therefore, we have solved \[\sqrt{529}=23\] by long division method.

Note: Students often get confused with division and dividend. So, the dividend is the number which is getting divided and it is placed inside and the divisor is the number which is dividing the dividend and it is placed outside. For better understanding, we can show the divisor, dividend, quotient and remainder as