# How do you find the square root of 6561?

Jun 8, 2016

$\sqrt{6561} = 81$

#### Explanation:

To find square root of $6561$, we should first factorize it.

From divisibility rules, it is apparent that it is divisible by $3$ and dividing by $3$, we get $2187$, which is again divisible by $3$ and dividing by $3$, we get $729$.

$729$ is clearly again divisible by $3$. Dividing by $3$, we get $243$, which is again divisible by $3$ and dividing it by $3$ we get $81$, which is clearly $3 \times 3 \times 3 \times 3$.

Hence, $6561 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3$ and hence

$\sqrt{6561} = \sqrt{\overline{3 \times 3} \times \overline{3 \times 3} \times \overline{3 \times 3} \times \overline{3 \times 3}}$

= $3 \times 3 \times 3 \times 3 = 81$