Simplify. Assume $$ y $$ is greater than or equal to zero. $$ \sqrt{75 y^{7}} $$

Question

UpStudy AI · Accepted Answer

To simplify $$ \sqrt{75 y^{7}} $$ with the assumption that $$ y \geq 0 $$:

1. **Factor the expression under the square root:**
   $$
   \sqrt{75 y^{7}} = \sqrt{25 \times 3 \times y^{6} \times y}
   $$

2. **Separate the square root into individual parts:**
   $$
   \sqrt{25} \times \sqrt{3} \times \sqrt{y^{6}} \times \sqrt{y}
   $$

3. **Simplify each part:**
   - $$ \sqrt{25} = 5 $$
   - $$ \sqrt{y^{6}} = y^{3} $$ (since $$ y \geq 0 $$)

4. **Combine the simplified parts:**
   $$
   5 \times y^{3} \times \sqrt{3y} = 5y^{3} \sqrt{3y}
   $$

**Final Simplified Form:**
$$
5 y^{3} \sqrt{3 y}
$$
$$ 5y^{3}\sqrt{3y} $$

Simplify. Assume is greater than or equal to zero.