make 80 in radical form an equivalent expression of an integer multiplied by a radical

To express \( 80 \) in radical form as an equivalent expression of an integer multiplied by a radical, we can break \( 80 \) into its prime factors and simplify.

1. Prime factorization of \( 80 \):  
   \[
   80 = 2^4 \times 5
   \]

2. Group the perfect squares inside the square root:
   \[
   \sqrt{80} = \sqrt{2^4 \times 5} = \sqrt{(2^2)^2 \times 5}
   \]

3. Simplify the perfect square part:
   \[
   \sqrt{80} = \sqrt{4^2 \times 5} = 4\sqrt{5}
   \]

So, the equivalent expression is:
\[
\sqrt{80} = 4\sqrt{5}
\]

Would you like more details or have any questions?

Here are some related questions for practice:
1. Express \( \sqrt{50} \) as an integer multiplied by a radical.
2. Simplify \( \sqrt{72} \) in radical form.
3. What is the simplified form of \( \sqrt{32} \)?
4. Convert \( \sqrt{18} \) into an integer times a radical.
5. Express \( \sqrt{45} \) in simplified radical form.

**Tip**: When simplifying radicals, always look for the largest perfect square that divides the number under the square root!

Learn how to simplify √80 by breaking it down into prime factors. This step-by-step solution uses prime factorization and properties of radicals to express the square root of 80 as an integer multiplied by a radical. Suitable for students in Grades 7-9.

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