Questions: Simplify. √(16 y^4) Assume that the variable y represents a positive real number.

Solution Steps

To simplify the square root of a perfect square monomial, we need to find the square root of each factor separately. For the given expression \(\sqrt{16 y^{4}}\), we can take the square root of 16 and the square root of \(y^4\) independently.

We start with the expression \(\sqrt{16 y^{4}}\).

The square root of the numerical part is calculated as follows: \[ \sqrt{16} = 4 \]

Next, we simplify the variable part: \[ \sqrt{y^{4}} = y^{\frac{4}{2}} = y^{2} \]

Combining both parts, we have: \[ \sqrt{16 y^{4}} = 4y^{2} \]

Final Answer