The problem asks us to find the square root of 729, which can be expressed as $\sqrt{729}$.

1. Problem Description

The problem asks us to find the square root of 729, which can be expressed as $\sqrt{729}$.

2. Solution Steps

To find the square root of 729, we can use prime factorization.

First, divide 729 by the smallest prime number, which is

2. 729 is not divisible by 2, so we try the next prime number, which is

3. $729 \div 3 = 243$

Now, divide 243 by

3. $243 \div 3 = 81$

Divide 81 by

3. $81 \div 3 = 27$

Divide 27 by

3. $27 \div 3 = 9$

Divide 9 by

3. $9 \div 3 = 3$

Divide 3 by

3. $3 \div 3 = 1$

So, the prime factorization of 729 is $3 \times 3 \times 3 \times 3 \times 3 \times 3 = 3^6$.

Therefore, $\sqrt{729} = \sqrt{3^6} = 3^{6/2} = 3^3 = 3 \times 3 \times 3 = 27$.

3. Final Answer

27