find the square root of the 6561 by long divison method

The Correct Answer and Explanation is:

To find the square root of 6561 by the long division method, follow these steps:

Step 1: Group the digits

Start by grouping the digits of the number into pairs, starting from the right. For 6561, the groups will be:

65 and 61.

Step 2: Find the first divisor

Find the largest number whose square is less than or equal to the first group (65). In this case, 8 * 8 = 64. So, the first divisor is 8.

Write 8 as the first digit of the square root. Subtract 82=648^2 = 6482=64 from 65 to get the remainder:

65 – 64 = 1.

Bring down the next pair of digits (61), making the new number 161.

Step 3: Double the divisor

Now, double the divisor (8) to get 16. This will be the first part of the new divisor.

Step 4: Find the next digit

Now, you need to find a digit to append to the divisor. Consider the number you have (161). You need to find a digit ddd such that:(160+d)×d≤161(160 + d) \times d \leq 161(160+d)×d≤161

Try d=1d = 1d=1:(160+1)×1=161(160 + 1) \times 1 = 161(160+1)×1=161

So, the next digit of the square root is 1.

Step 5: Subtract and finish

Now, subtract 161161161 from 161161161 to get 0, and we are left with no remainder.

Thus, the square root of 6561 is 81.

Final Answer:

6561=81\sqrt{6561} = 816561=81

Explanation:

The long division method for finding square roots involves iterative steps of guessing and refining the divisor. You start by grouping the digits and progressively find the largest possible divisor that works, adding one digit at a time. This process ensures an accurate square root is obtained, in this case, 81.