Simplify Square Root Expression: √(144x^8/16x^2)

To solve this problem, we will follow these steps:

• Step 1: Simplify the fraction under the square root.
• Step 2: Apply the square root property to the simplified result.
• Step 3: Simplify the final expression.

Now, let’s work through each step:

Step 1: Simplify the fraction $\frac{144x^8}{16x^2}$.

Divide the coefficients: $\frac{144}{16} = 9$.

Subtract the exponents of $x$: $x^{8-2} = x^6$.

Thus, the simplified fraction is $9x^6$.

Step 2: Apply the square root property on $9x^6$.

The square root of a product is the product of the square roots, so we have:

$\sqrt{9x^6} = \sqrt{9} \cdot \sqrt{x^6}$.

Step 3: Simplify the result.

$\sqrt{9} = 3$.

$\sqrt{x^6} = x^{\frac{6}{2}} = x^3$.

Therefore, the expression simplifies to $3x^3$.

Thus, the solution to the problem is $3x^3$.