Questions: Simplify. Assume all variables are positive. √(36 t^3 / 3 x^2)=

Solution Steps

To simplify the given expression, we can follow these steps:

1. Simplify the fraction inside the square root.
2. Separate the square root of the numerator and the denominator.
3. Simplify the square roots of the individual terms.

First, we simplify the fraction inside the square root: \[ \frac{36 t^3}{3 x^2} = \frac{36}{3} \cdot \frac{t^3}{x^2} = 12 \cdot \frac{t^3}{x^2} \]

Next, we separate the square root of the numerator and the denominator: \[ \sqrt{12 \cdot \frac{t^3}{x^2}} = \sqrt{12} \cdot \sqrt{\frac{t^3}{x^2}} \]

We then simplify the square roots of the individual terms: \[ \sqrt{12} = 2\sqrt{3} \] \[ \sqrt{\frac{t^3}{x^2}} = \frac{\sqrt{t^3}}{\sqrt{x^2}} = \frac{t^{3/2}}{x} \]

Finally, we combine the simplified terms: \[ 2\sqrt{3} \cdot \frac{t^{3/2}}{x} = \frac{2\sqrt{3} \cdot t^{3/2}}{x} \]

Final Answer