Simplify.

Question

√81y^6
Assume that the variable y represents a positive real number.

Answer 1

To simplify the expression \(\sqrt{81y^6}\), we can break it down into two parts: the square root of the numerical part and the square root of the variable part.

1. Start with the numerical part: \[ \sqrt{81} = 9 \]

2. Next, simplify the variable part: \[ \sqrt{y^6} = y^{6/2} = y^3 \]

Now, we can combine both parts: \[ \sqrt{81y^6} = \sqrt{81} \cdot \sqrt{y^6} = 9y^3 \]

Therefore, the simplified expression is: \[ \boxed{9y^3} \]