Question

How do you find the square root $6561$?

Answer 1

Find the square root using prime factorization method:

Given number, $6561$

The square root of $6561$ is

$\begin{array}{rcl}6561& =& 3\times 3\times 3\times 3\times 3\times 3\times 3\times 3\left[\because 6561÷3=2187,2187÷3=729,729÷3=243,243÷3=81,81÷3=27,27=3^3\right]\\ & \Rightarrow & \sqrt{6561}=\sqrt{3\times 3\times 3\times 3\times 3\times 3\times 3\times 3}\\ & \Rightarrow & \sqrt{6561}=3\times 3\times 3\times 3\\ & \Rightarrow & \sqrt{6561}=81\end{array}$

Hence, the square root of $\mathbf{6561}$ is $\mathbf{81}$.