simplify the expression completely: square root of 12x^2 - square root of 9x^4

To simplify the expression \(\sqrt{12x^2} - \sqrt{9x^4}\), follow these steps:

1. **Simplify each square root separately:**

   - \(\sqrt{12x^2}\) can be simplified as follows:
     \[
     \sqrt{12x^2} = \sqrt{4 \cdot 3 \cdot x^2} = \sqrt{4} \cdot \sqrt{3} \cdot \sqrt{x^2} = 2 \cdot \sqrt{3} \cdot x = 2x\sqrt{3}
     \]

   - \(\sqrt{9x^4}\) can be simplified as follows:
     \[
     \sqrt{9x^4} = \sqrt{9} \cdot \sqrt{x^4} = 3 \cdot x^2 = 3x^2
     \]

2. **Subtract the simplified expressions:**

   \[
   2x\sqrt{3} - 3x^2
   \]

This is the simplified form of the expression.

### Final Answer:
\[
\sqrt{12x^2} - \sqrt{9x^4} = 2x\sqrt{3} - 3x^2
\]

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

Here are 5 related questions:

1. How do you simplify \(\sqrt{18x^3}\)?
2. What is the process for simplifying \(\sqrt{8x^6} - \sqrt{2x^4}\)?
3. How do you handle expressions involving cube roots like \(\sqrt[3]{27x^6}\)?
4. How does the square root of a product differ from the square root of a sum?
5. What are the steps to rationalize a denominator with a square root?

**Tip:** When simplifying square roots, always look for perfect square factors first to make the process easier.

Learn how to simplify the expression \(\sqrt{12x^2} - \sqrt{9x^4}\) step-by-step with detailed explanations and examples. This problem covers algebraic manipulation involving square roots and is suitable for Grades 7-9 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