Simplify. Assume \( q \) is greater than or equal to zero. \( \sqrt{12 q^{10}} \)

To simplify \( \sqrt{12 q^{10}} \) with the assumption that \( q \geq 0 \), follow these steps: 1. **Factor the expression inside the square root:** \[ \sqrt{12 q^{10}} = \sqrt{4 \times 3 \times q^{10}} \] 2. **Simplify the square roots of the perfect squares:** - \( \sqrt{4} = 2 \) - \( \sqrt{q^{10}} = q^{10/2} = q^5 \) (since \( q \geq 0 \), we don't need to consider the negative root) 3. **Combine the simplified parts:** \[ \sqrt{12 q^{10}} = 2 \times q^5 \times \sqrt{3} = 2 q^5 \sqrt{3} \] **Final Answer:** \[ 2 q^{5} \sqrt{3} \]