To simplify \( 3\sqrt[5]{24q} \), we'll break it down step by step.

### Step 1: Factor inside the radical
The expression inside the 5th root is \( 24q \). Let's factor \( 24 \):

\[
24 = 2^3 \times 3
\]

So the expression becomes:

\[
3\sqrt[5]{2^3 \times 3 \times q}
\]

### Step 2: Simplify the 5th root
Since none of the factors inside the radical have powers greater than or equal to 5, they cannot be simplified further at this point.

Thus, the expression remains:

\[
3\sqrt[5]{24q}
\]

This is the simplified form of the given expression.

---

Would you like more details or have any questions? Here are five related questions:

1. How do you simplify higher roots involving variables?
2. What are some properties of radicals that can help in simplification?
3. How would the process change if the exponent were a square root instead?
4. How do you simplify cube roots in terms of algebraic expressions?
5. How do you factor numbers and variables under radicals effectively?

**Tip**: Always check for factors that have powers matching the root when simplifying expressions under a radical.

Learn how to simplify the expression 3√24q to the 5th power step by step. This explanation breaks down factoring 24 and simplifying radicals using key algebraic concepts. Ideal for high school students (Grades 9-11).

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation