What is the cube root of 729?

We divide 729 by the smallest prime number, which is 3.

$$729 \div 3 = 243$$ $$243 \div 3 = 81$$ $$81 \div 3 = 27$$ $$27 \div 3 = 9$$ $$9 \div 3 = 3$$ $$3 \div 3 = 1$$

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

To find the cube root, we group the identical prime factors in sets of three.

$$729 = (3 \times 3 \times 3) \times (3 \times 3 \times 3)$$ $$729 = 3^3 \times 3^3$$

$$\sqrt[3]{729} = \sqrt[3]{3^3 \times 3^3}$$ $$\sqrt[3]{729} = 3 \times 3$$ $$\sqrt[3]{729} = 9$$

The cube root of 729 is 9.

$$9$$