Express in simplest radical form.

square root of, 180, end square root

180​


To simplify the square root of 180, we begin by finding the prime factorization of 180:

\[
180 = 2^2 \times 3^2 \times 5
\]

Now, break it down:

\[
\sqrt{180} = \sqrt{2^2 \times 3^2 \times 5}
\]

Next, apply the square root to the perfect squares:

\[
\sqrt{2^2} = 2 \quad \text{and} \quad \sqrt{3^2} = 3
\]

So,

\[
\sqrt{180} = 2 \times 3 \times \sqrt{5} = 6\sqrt{5}
\]

Thus, the simplest radical form of \(\sqrt{180}\) is:

\[
6\sqrt{5}
\]

Would you like more details or have any questions?

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Here are 5 related questions you can explore:
1. How do you simplify \(\sqrt{72}\)?
2. What is the square root of 50 in simplest radical form?
3. How can you simplify \(\sqrt{245}\)?
4. What is the prime factorization method for simplifying radicals?
5. How do you simplify \(\sqrt{32}\)?

**Tip**: Always look for perfect square factors when simplifying square roots!

Express in simplest radical form: square root of 180.

Discover how to simplify the square root of 180 using prime factorization. Learn the step-by-step process of breaking down square roots, applying the square root property, and writing the final solution in simplest radical form. Ideal for Grades 8-10 students.

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