Square Root of 6561 Calculation

The question asks for the square root of 6561, denoted mathematically as $\sqrt{6561}$. We need to find a number which, when multiplied by itself, yields 6561.

Square Root Estimation

1. Estimate the range: Consider perfect squares around 6561. We know $80^2 = 80 \times 80 = 6400$ and $90^2 = 90 \times 90 = 8100$. Since $6400 < 6561 < 8100$, the square root of 6561 must lie between 80 and 90.
2. Analyze the last digit: The number 6561 ends with the digit 1. An integer's square ends in 1 only if the integer itself ends in 1 or 9 (because $1^2 = 1$ and $9^2 = 81$, which ends in 1).
3. Identify potential candidates: Based on the range (80-90) and the last digit analysis (ending in 1 or 9), the possible candidates for the square root are 81 and 89.
4. Test the candidates:
   • Calculate $81 \times 81$. This equals 6561.
   • Calculate $89 \times 89$. This equals 7921.
5. Determine the result: Since $81 \times 81 = 6561$, the square root of 6561 is 81.

Square Root Result

The square root of 6561 is 81.