Express in simplest radical form.

square root of, 45, end square root

45​


To simplify the square root of 45, we start by factoring 45 into its prime factors:

\[
45 = 9 \times 5 = 3^2 \times 5
\]

Now, apply the square root:

\[
\sqrt{45} = \sqrt{3^2 \times 5} = 3 \sqrt{5}
\]

Thus, the simplest radical form of \( \sqrt{45} \) is:

\[
3 \sqrt{5}
\]

Would you like a detailed breakdown, or do you have any questions?

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Here are related questions to deepen understanding:

1. What is the simplest radical form of \( \sqrt{50} \)?
2. How do we simplify \( \sqrt{75} \)?
3. Why do we only simplify perfect squares within a square root?
4. How can we simplify \( \sqrt{12} \)?
5. What steps should we follow to simplify any square root?

**Tip:** Always look for perfect square factors when simplifying square roots to ensure you reach the simplest form.

Express in simplest radical form. square root of, 45, end square root

Learn to simplify the square root of 45 to its simplest radical form with step-by-step guidance. This problem explores prime factorization and simplifying square roots, ideal for students in Grades 6-8.

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