Simplify the expression. (Assume that all variables are positive.) $$ \sqrt{\frac{121 x^{3}}{49 x}} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression:

$$
\sqrt{\frac{121 x^{3}}{49 x}}
$$

**Step 1: Simplify the Fraction Inside the Square Root**

$$
\frac{121 x^{3}}{49 x} = \frac{121}{49} \cdot \frac{x^3}{x} = \frac{121}{49} \cdot x^{2}
$$

**Step 2: Apply the Square Root to Both Parts**

$$
\sqrt{\frac{121}{49} \cdot x^{2}} = \sqrt{\frac{121}{49}} \cdot \sqrt{x^{2}} = \frac{11}{7} \cdot x
$$

**Final Simplified Expression:**

$$
\frac{11x}{7}
$$

**Answer:** $$\dfrac{11\,x}{7}$$
The simplified expression is $$\frac{11x}{7}$$.

Simplify the expression. (Assume that all variables are positive.)