Add or subtract terms whenever possible.

3 RootIndex 5 StartRoot 64 EndRoot plus RootIndex 5 StartRoot 486 EndRoot

Let's simplify and solve the given expression:

\[ 3 \sqrt[5]{64} + \sqrt[5]{486} \]

### Step 1: Simplify the radicals

1. \(\sqrt[5]{64}\):
   - \(64 = 2^6\), and taking the fifth root of 64 gives us:
   \[
   \sqrt[5]{64} = 2
   \]

2. \(\sqrt[5]{486}\):
   - \(486 = 2 \times 3^5\), so:
   \[
   \sqrt[5]{486} = 3
   \]

### Step 2: Substitute the simplified values
\[
3 \times 2 + 3 = 6 + 3 = 9
\]

### Final Answer:
\[
9
\]

Would you like more details on any of these steps or have any questions?

Here are 5 related questions:
1. How do you calculate roots with different indices?
2. What is the difference between square roots and cube roots?
3. How can you break down larger numbers into prime factors?
4. What are some real-life applications of radicals?
5. How do you handle radicals with variables?

**Tip:** When simplifying radicals, always check if the number can be factored into smaller powers to make calculations easier.

Learn how to simplify the expression 3√⁵64 + √⁵486 using radical properties and simplification techniques. This step-by-step guide explains how to handle fifth roots and provides insights into radical simplifications. Suitable for students in Grades 9-10.

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