Solve the Square Root Expression: Simplifying √(196x²/49)

To solve this problem, we'll apply these steps:

• Step 1: Simplify the fraction $\frac{196x^2}{49}$.
• Step 2: Apply the square root quotient property.
• Step 3: Simplify each term to find the final simplified form.

Now, let's perform each step:

Step 1: Simplify the fraction inside the square root:

$\frac{196x^2}{49} = \frac{196}{49} \times x^2$

Simplify $\frac{196}{49}$: Since $196 \div 49 = 4$, we have $\frac{196}{49} = 4$.

The expression therefore simplifies to $4x^2$.

Step 2: Apply the square root quotient property:

$\sqrt{4x^2} = \sqrt{4} \times \sqrt{x^2}$

Step 3: Simplify each term:

$\sqrt{4} = 2$ and $\sqrt{x^2} = x$ (assuming $x \geq 0$).

Therefore, the expression simplifies to $2x$.

Thus, the solution to the problem is $\boxed{2x}$.