What is the square root of 2601 using the long division method?

• A) 53
• B) 52
• C) 51
• D) 56

The square root of 2601 can be found using the long division method, which is a systematic way to calculate square roots. Here’s how to do it step by step:

Step 1: Set Up the Problem

First, pair the digits of the number from right to left. For 2601, we have:

• 26 | 01

Step 2: Find the Largest Square

Look for the largest square number less than or equal to 26. The largest square is 25 (which is 5 squared).

Write 5 above the line and subtract 25 from 26:

• 26 - 25 = 1

Step 3: Bring Down the Next Pair

Next, bring down the next pair of digits (01) next to the remainder:

• 1 | 01 = 101

Step 4: Double the Quotient

Double the number above the line (5) to get 10. Now, we need to find a digit (let's call it X) such that:

• 10X * X is less than or equal to 101

Testing with 1, we find:

• 101 * 1 = 101

This works, so we place 1 next to 5, making it 51.

Step 5: Final Calculation

Now, subtract 101 from 101:

• 101 - 101 = 0

Since there are no more pairs to bring down, we have completed the calculation.

Final Result

The square root of 2601 is 51. Therefore, the correct answer is:

C) 51