https://file.aiquickdraw.com/mathbot/file/1722438646502d9qonbtz.jpeg

Breng samen onder 1 wortel en vereenvoudig door zoveel mogelijk buiten het wortelteken te brengen:

To simplify the given expression \(\sqrt{2 \cdot a^8}\), follow these steps:

1. **Combine under one radical:**
   \[
   \sqrt{2 \cdot a^8}
   \]

2. **Express the product inside the radical:**
   \[
   \sqrt{2} \cdot \sqrt{a^8}
   \]

3. **Simplify \(\sqrt{a^8}\):**
   Since \(a^8\) is a perfect square, \(\sqrt{a^8} = a^{8/2} = a^4\).

4. **Combine the simplified terms:**
   \[
   \sqrt{2} \cdot a^4
   \]

So, the simplified form of \(\sqrt{2 \cdot a^8}\) is:
   \[
   a^4 \cdot \sqrt{2}
   \]

Would you like further details or have any questions?

Here are some related questions to further your understanding:

1. How would you simplify \(\sqrt{50 \cdot b^6}\)?
2. Can you explain the properties of square roots used in the simplification process?
3. What is the simplified form of \(\sqrt{72 \cdot x^{10}}\)?
4. How would you handle \(\sqrt{18 \cdot y^9}\) if \(y\) is a variable?
5. How can you simplify \(\sqrt{3a^6 \cdot b^4}\)?
6. How do you simplify \(\sqrt{4x^8 \cdot 9y^6}\)?
7. What steps would you follow to simplify \(\sqrt{8c^5 \cdot 2d^7}\)?
8. Can you describe the process of simplifying \(\sqrt{27 \cdot z^12}\)?

**Tip:** When simplifying square roots, always look for perfect squares inside the radical to simplify your expression more efficiently.

Learn how to simplify the expression \(\sqrt{2 \cdot a^8}\) by combining terms under one radical and simplifying. This problem involves square roots and simplification techniques, suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation