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

To find the square root of 529 using the long division method, follow these steps:

Step 1: Group the digits in pairs from right to left
We start by pairing the digits of 529. Since it has three digits, we make two groups:

5 (the first digit) and 29 (the last two digits).
Step 2: Find the largest number whose square is less than or equal to the first group (5)
We start with the first group, 5. The largest number whose square is less than or equal to 5 is 2, because 2² = 4, and 3² = 9 (which is greater than 5).

Write 2 above the line as the first digit of the square root.

Now subtract 4 (2²) from 5: 5 - 4 = 1

Step 3: Bring down the next pair (29)
Next, bring down the next pair of digits, 29. Now you have 129.

Step 4: Double the current result (2)
Double the current result (2), which gives 4. Now, think of a number to append next to 4 to form a new divisor such that when multiplied by the same digit, the product is less than or equal to 129.

The number we append is 7 (forming the divisor 47), because: 47 × 7 = 329 (which is greater than 129).

Now, try with 4, which forms the divisor 44: 44 × 4 = 176 (which is still less than 129).

So, the next digit is 4, forming a divisor of 44