To simplify the square root of 72:

$\sqrt{72}$

1. First, break down 72 into its prime factors: $72 = 2^3 \times 3^2$

2. Apply the square root to the prime factorization: $\sqrt{72} = \sqrt{2^3 \times 3^2}$

3. Separate the perfect squares from the non-perfect squares: $\sqrt{72} = \sqrt{(2^2 \times 3^2) \times 2} = \sqrt{2^2 \times 3^2} \times \sqrt{2}$

4. Take the square root of the perfect squares: $\sqrt{72} = 6\sqrt{2}$

Thus, the simplified form of $\sqrt{72}$ is:

$\boxed{6\sqrt{2}}$

Would you like more details or have any questions?

Here are five related questions:

1. How do you simplify $\sqrt{128}$?
2. Can you explain the steps for simplifying $\sqrt{50}$?
3. What are the prime factors of 90, and how would you simplify $\sqrt{90}$?
4. How do you simplify the square root of a number like $\sqrt{18}$?
5. What is the simplified form of $\sqrt{200}$?

Tip: Always check for perfect squares when simplifying square roots; it helps break down the expression easily.