Simplify Square Root Expression: √(64x⁴/16x²)

Solve the following exercise:

$\sqrt{\frac{64x^4}{16x^2}}=$

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

• Step 1: Simplify the expression inside the square root.
• Step 2: Apply the square root property to the simplified expression.
• Step 3: Confirm the result with the answer choices.

Now, let's work through each step:

Step 1: Simplify the expression inside the square root:
We have $\frac{64x^4}{16x^2}$. Divide the coefficients and the powers of $x$:
$\frac{64}{16} = 4$ and using exponents, $\frac{x^4}{x^2} = x^{4-2} = x^2$.
Therefore, $\frac{64x^4}{16x^2} = 4x^2$.

Step 2: Apply the square root property:
$\sqrt{4x^2} = \sqrt{4} \cdot \sqrt{x^2} = 2 \cdot x = 2x$.

Therefore, the solution to the problem is $2x$.