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.

Learn how to simplify the square root of 72 by breaking it down into prime factors. This step-by-step solution explains how to apply square root properties and simplify the expression to 6√2. Ideal for students in Grades 7-9.

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