Question: Simplify.
$$\sqrt{81y^6}$$
Assume that the variable $y$ re
1. **State the problem:** Simplify the expression $$\sqrt{81y^6}$$.
2. **Recall the formula:** The square root of a product is the product of the square roots: $$\sqrt{a b} = \sqrt{a} \times \sqrt{b}$$.
3. **Apply the formula:**
$$\sqrt{81y^6} = \sqrt{81} \times \sqrt{y^6}$$
4. **Simplify each part:**
- $$\sqrt{81} = 9$$ because $$9^2 = 81$$.
- $$\sqrt{y^6} = y^{\frac{6}{2}} = y^3$$ by the rule $$\sqrt{x^n} = x^{\frac{n}{2}}$$.
5. **Combine the results:**
$$9 \times y^3 = 9y^3$$
**Final answer:** $$\boxed{9y^3}$$