$$  $$simplify $$ \sqrt{80}\text{ } $$to the form $$ a\sqrt{b} $$

To simplify $ \sqrt{80} $ into the form $ a\sqrt{b} $, follow these steps:

1. Find the prime factorization of 80:
   \[
   80 = 2^4 \times 5
   \]

2. Rewrite $ \sqrt{80} $ as $ \sqrt{2^4 \times 5} $.

3. Split the square root:
   \[
   \sqrt{80} = \sqrt{2^4} \times \sqrt{5}
   \]

4. Simplify $ \sqrt{2^4} $:
   \[
   \sqrt{2^4} = 2^2 = 4
   \]

5. Now, you have:
   \[
   \sqrt{80} = 4\sqrt{5}
   \]

Thus, $ \sqrt{80} $ simplified is $ 4\sqrt{5} $.

### Would you like further details on this solution or have any questions?

Here are 5 related questions you might want to explore:
1. How would you simplify $ \sqrt{200} $?
2. Can you express $ \sqrt{18} $ in the form $ a\sqrt{b} $?
3. What is the simplified form of $ \sqrt{50} $?
4. How would you solve $ \sqrt{72} $ to $ a\sqrt{b} $?
5. How do you simplify the expression $ 3\sqrt{45} $?

**Tip:** When simplifying square roots, always look for perfect squares within the radicand to simplify the expression efficiently.

simplify $ \sqrt{80} $ to the form $ a\sqrt{b} $

Learn how to simplify $ \sqrt{80} $ into the form $ a\sqrt{b} $ using prime factorization and the product property of square roots. This problem is suitable for students in Grades 6-8 and covers key concepts like square root simplification and factorization.

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