find the number of square root in division method for 486

The Correct Answer and Explanation is:

To find the square root of 486 using the long division method, we first determine the number of digit pairs in the number 486 from right to left.

✅ Step 1: Group the digits into pairs

We begin from the right side:

486 → written as 4 | 86

Thus, the number 486 has 2 digit groups (also referred to as 2 steps or 2 digits in the square root result using the division method).

✅ Final Answer:

Number of digits in the square root of 486 using the division method = 2

📘 Detailed Explanation (like in textbooks):

The long division method of finding square roots involves pairing the digits of the number, starting from the right. Each pair of digits helps determine one digit of the square root.

Let’s understand this in steps using 486:

Step 1: Group the number

Break the number into pairs of digits starting from the right:

For 486, we write it as 4 | 86
So, we have two digit groups: “4” and “86”

👉 The number of digit groups tells us how many steps we will perform and how many digits the square root will contain.

Step 2: Find the largest square ≤ 4

The largest square less than or equal to 4 is 2² = 4
Write 2 as the first digit of the root.

Step 3: Subtract and bring down the next pair

4 − 4 = 0
Bring down 86

Now use the long division method to estimate the next digit using double the previous digit and finding a suitable digit to append.

Step 4: Continue the division

Double of 2 is 4. Now we try 41 × 1 = 41, 42 × 2 = 84, 43 × 3 = 129…
The best fit is 42 × 2 = 84. Subtract 86 − 84 = 2

So, the square root of 486 by division method up to two decimal digits is 22.02 approximately.

📌 Conclusion:

Since 486 has two digit groups, its square root by division method will have 2 digits before the decimal point. Therefore, the number of digits (or steps) in the square root is 2.