Simplify the square root.

StartRoot 325 EndRoot325

Question content area bottom

Part 1

StartRoot 325 EndRoot325equals=5 StartRoot 13 EndRoot513

​(Type an exact​ answer, using radicals as​ needed.)

To simplify \( \sqrt{325} \), follow these steps:

1. Start by factoring 325 into its prime factors:
   \[
   325 = 5^2 \times 13
   \]

2. Now, apply the square root to the factors:
   \[
   \sqrt{325} = \sqrt{5^2 \times 13}
   \]

3. Since \( \sqrt{5^2} = 5 \), you can simplify further:
   \[
   \sqrt{325} = 5 \sqrt{13}
   \]

Thus, the simplified form of \( \sqrt{325} \) is:
\[
\boxed{5 \sqrt{13}}
\]

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. How do you simplify square roots with larger numbers?
2. What are the prime factors of 400?
3. How do you simplify \( \sqrt{450} \)?
4. How can you estimate the value of \( \sqrt{13} \)?
5. Why is \( \sqrt{25} = 5 \)?

**Tip:** When simplifying square roots, always check if the number inside the root has perfect square factors!

Simplify the square root of 325: \( \sqrt{325} \).

Learn how to simplify \( \sqrt{325} \) step-by-step by using prime factorization and applying square root properties. This problem covers the concepts of simplifying radicals and prime factorization, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation