Simplify. Assume $$ q $$ is greater than or equal to zero. $$ \sqrt{18 q^{4}} $$

Question

UpStudy AI · Accepted Answer

To simplify $$ \sqrt{18 q^{4}} $$ with the assumption that $$ q \geq 0 $$, follow these steps:

1. **Factor the expression inside the square root:**
   $$
   \sqrt{18 q^{4}} = \sqrt{9 \times 2 \times q^{4}}
   $$

2. **Separate the square root of each factor:**
   $$
   \sqrt{9 \times 2 \times q^{4}} = \sqrt{9} \times \sqrt{2} \times \sqrt{q^{4}}
   $$

3. **Simplify each square root individually:**
   - $$ \sqrt{9} = 3 $$
   - $$ \sqrt{q^{4}} = q^{2} $$ (since $$ q \geq 0 $$)

4. **Combine the simplified terms:**
   $$
   3 \times q^{2} \times \sqrt{2} = 3 q^{2} \sqrt{2}
   $$

**Final Simplified Form:**
$$
3 q^{2} \sqrt{2}
$$
$$ 3 q^{2} \sqrt{2} $$

Simplify. Assume is greater than or equal to zero.