Simplify sqrt(36x⁴)/sqrt(x²): Square Root Fraction Problem

Solve the following exercise:

$\frac{\sqrt{36x^4}}{\sqrt{x^2}}=$

To solve the problem, we will simplify the expression step-by-step:

• Step 1: Simplify $\sqrt{36x^4}$
  We know that $\sqrt{36x^4}$ can be rewritten as $\sqrt{36} \cdot \sqrt{x^4}$.
  First, simplify $\sqrt{36}$:
  $\sqrt{36} = 6$ because $6^2 = 36$.
  Next, simplify $\sqrt{x^4}$:
  $\sqrt{x^4} = x^2$ because $(x^2)^2 = x^4$.
• Step 2: Simplify $\sqrt{x^2}$
  $\sqrt{x^2} = x$ (assuming $x \geq 0$ to avoid absolute values).
• Step 3: Simplify the expression $\frac{\sqrt{36x^4}}{\sqrt{x^2}}$
  Substitute the values obtained in the above steps:
  $\frac{\sqrt{36x^4}}{\sqrt{x^2}} = \frac{6x^2}{x}$.
  The expression simplifies to $6x$ as $\frac{x^2}{x} = x$.

Therefore, the solution to the problem is $6x$, which matches choice 4.