Questions: Algebra and Geometry Review Simplifying a radical expression with an odd exponent Simplify. √(16 y^5) Assume that the variable represents a positive real number.

Solution Steps

To simplify the radical expression \(\sqrt{16 y^{5}}\), we can break it down into two parts: the square root of the constant and the square root of the variable expression. The square root of 16 is straightforward, and for the variable part, we can use the property that \(\sqrt{y^5} = y^{5/2}\). We can then express \(y^{5/2}\) as \(y^2 \cdot \sqrt{y}\).

We start with the expression \( \sqrt{16 y^{5}} \). This can be separated into two parts: the constant and the variable.

The square root of the constant \( 16 \) is calculated as follows: \[ \sqrt{16} = 4 \]

Next, we simplify the variable part \( \sqrt{y^{5}} \). Using the property of exponents, we have: \[ \sqrt{y^{5}} = y^{5/2} \]

Combining the results from the constant and variable simplifications, we get: \[ \sqrt{16 y^{5}} = 4 y^{5/2} \]

Final Answer