Find the square root of :
`4761`

Answer

To find the square root of 4761 using prime factorization, we will follow these steps:

### Step 1: Prime Factorization
We start by dividing 4761 by the smallest prime number, which is 3.

- **Calculation**:
\[ 4761 \div 3 = 1587 \]

### Step 2: Continue Prime Factorization
Next, we continue factoring 1587 by 3 again.

- **Calculation**:
\[ 1587 \div 3 = 529 \]

### Step 3: Factor 529
Now we need to factor 529. The next prime number is 23.

- **Calculation**:
\[ 529 \div 23 = 23 \]

### Step 4: Write the Prime Factorization
Now we can write the complete prime factorization of 4761:
\[ 4761 = 3^2 \times 23^2 \]

### Step 5: Apply the Square Root
To find the square root, we take the square root of each factor:
\[ \sqrt{4761} = \sqrt{3^2 \times 23^2} = \sqrt{3^2} \times \sqrt{23^2} = 3 \times 23 \]

### Step 6: Final Calculation
Now we multiply the results:
\[ 3 \times 23 = 69 \]

### Conclusion
Thus, the square root of 4761 is:
\[ \sqrt{4761} = 69 \]

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