To simplify the square root of 80, we can follow these steps:

1. **Factor 80 into its prime factors**:
   \[
   80 = 2 \times 40 = 2 \times 2 \times 20 = 2 \times 2 \times 2 \times 10 = 2 \times 2 \times 2 \times 2 \times 5 = 2^4 \times 5
   \]

2. **Apply the square root to the factors**:
   \[
   \sqrt{80} = \sqrt{2^4 \times 5}
   \]

3. **Simplify by taking the square root of perfect squares**:
   \[
   \sqrt{2^4 \times 5} = \sqrt{2^4} \times \sqrt{5} = 2^2 \times \sqrt{5} = 4\sqrt{5}
   \]

So, the simplified form of \( \sqrt{80} \) is \( 4\sqrt{5} \).

Would you like any further details or have any questions?

Here are some related questions for further practice:
1. How would you simplify \( \sqrt{45} \)?
2. What is \( \sqrt{180} \) in its simplest form?
3. If \( \sqrt{x} = 7 \sqrt{5} \), what is the value of \( x \)?
4. Simplify \( \sqrt{50} \).
5. How would you write \( \sqrt{128} \) as a product of a whole number and a square root?
6. What is the simplified form of \( \sqrt{98} \)?
7. Can \( \sqrt{a} \) be simplified further if \( a = 200 \)?
8. What is the square root of 72 in simplest radical form?

**Tip:** When simplifying square roots, always factor the number into its prime factors and look for perfect squares!

Learn how to simplify the square root of 80 (sqrt(80)) with a detailed step-by-step guide. This problem involves prime factorization and simplifying square roots. Suitable for students in Grades 7-9.

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