Solve the Square Root Expression: Simplifying √(25x^4)

To solve the expression $\sqrt{25x^4}$, we will use the product property of square roots.

First, separate the expression inside the square root into two parts:
$\sqrt{25x^4} = \sqrt{25} \cdot \sqrt{x^4}$.

Next, simplify each square root:

• $\sqrt{25} = 5$ because $5^2 = 25$.
• $\sqrt{x^4} = x^{4/2} = x^2$ since the square root of $x^n$ is $x^{n/2}$ for even $n$.

Now combine the simplified terms:
$5 \cdot x^2$.

Therefore, the simplified expression is $5x^2$.

The correct answer is therefore $\mathbf{5x^2}$, which corresponds to choice $2$.