Find the `sqrt(2601)`

Answer

To find the square root of 2601, we can follow these steps:

### Step 1: Write down the number
First, we write the number we want to find the square root of:
\[ 2601 \]

### Step 2: Separate the number into pairs
Next, we separate the digits of the number into pairs starting from the right. This gives us:
\[ 26 \quad 01 \]

### Step 3: Analyze the last pair
The last pair is 01. We need to determine which digits can form a square number that ends with 1. The possible digits are:
- \( 1^2 = 1 \)
- \( 9^2 = 81 \)

Thus, the last digit of the square root can be either 1 or 9.

### Step 4: Analyze the first pair
Now, we look at the first pair, which is 26. We need to find two perfect squares between which 26 lies:
- \( 5^2 = 25 \)
- \( 6^2 = 36 \)

Since 26 is closer to 25, we will consider the digit 5 for the tens place of our potential square root.

### Step 5: Combine the results
From the analysis, we have:
- The last digit can be either 1 or 9.
- The first digit is 5.

Thus, the possible square roots could be 51 or 59. Since 26 is closer to 25, we choose:
\[ 51 \]

### Step 6: Verify the result
To confirm, we can square 51:
\[ 51 \times 51 = 2601 \]

This verifies that our answer is correct.

### Final Answer:
The square root of 2601 is:
\[ \sqrt{2601} = 51 \]

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