Express in simplest radical form.square root of, 4, x, squared, end square root4x 2 ​

1. Break Down the Problem

We need to simplify the expression $\sqrt{4x^2}$.

2. Relevant Concepts

To simplify a square root, we utilize the property:
$\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$
Additionally, for any positive real number $a$, $\sqrt{x^2} = |x|$.

3. Analysis and Detail

Now, we can apply the aforementioned property:
$\sqrt{4x^2} = \sqrt{4} \cdot \sqrt{x^2}$
Calculating each part:

• $\sqrt{4} = 2$
• $\sqrt{x^2} = |x|$

Combining these gives us: $\sqrt{4x^2} = 2 \cdot |x|$

4. Verify and Summarize

The expression has been simplified correctly, and the result is verified based on the properties of square roots.

Final Answer

The simplest radical form of $\sqrt{4x^2}$ is:
$2|x|$