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To fully simplify \( \sqrt{90} \), we need to find the prime factorization of 90.

First, express 90 as a product of prime factors:
\[
90 = 2 \times 3^2 \times 5
\]

Now, break the square root into parts:
\[
\sqrt{90} = \sqrt{2 \times 3^2 \times 5}
\]

Since \( 3^2 \) is a perfect square, we can take 3 out of the square root:
\[
\sqrt{90} = 3\sqrt{2 \times 5} = 3\sqrt{10}
\]

Thus, the fully simplified form of \( \sqrt{90} \) is:
\[
\boxed{3\sqrt{10}}
\]

Would you like further details, or do you have any questions?

Here are 5 related questions:
1. How would you simplify \( \sqrt{72} \)?
2. Can you express \( \sqrt{45} \) in its simplest form?
3. How can prime factorization help simplify square roots?
4. What happens if you try to simplify \( \sqrt{200} \)?
5. What is the simplest form of \( \sqrt{50} \)?

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

Learn how to fully simplify the square root of 90 by using prime factorization. This problem covers key mathematical concepts like square root properties and prime factorization. Perfect for students in Grades 7-9.

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