Simplify. Assume 5 and \( t \) are greater than or equal to zero. \( \sqrt{147 s^{3} t^{4}} \)

To simplify \( \sqrt{147 s^{3} t^{4}} \), we can break it down step by step. First, notice that 147 can be factored into \( 49 \times 3 \), where \( 49 \) is a perfect square. So, we have: \[ \sqrt{147 s^{3} t^{4}} = \sqrt{49 \cdot 3 \cdot s^{3} \cdot t^{4}} \] Next, we can separate the square roots: \[ \sqrt{49} \cdot \sqrt{3} \cdot \sqrt{s^3} \cdot \sqrt{t^4} \] Calculating the square roots gives us: \[ 7 \cdot \sqrt{3} \cdot \sqrt{s^3} \cdot t^2 \] Now, for \( \sqrt{s^3} \), we can simplify it as follows: \[ \sqrt{s^3} = \sqrt{s^2 \cdot s} = s \sqrt{s} \] Plugging this back into our expression, we obtain: \[ 7 \cdot t^2 \cdot s \cdot \sqrt{3s} \] Thus, the final simplified result is: \[ 7st^2 \sqrt{3s} \]