Question

1. perform the indicated operation on each radical expression and simplify completely. a. $3sqrt{xy^3} + 8sqrt{xy^3}$

Explanation:

Step1: Simplify each radical

We know that $\sqrt{xy^3}=\sqrt{x\cdot y^2\cdot y}=y\sqrt{xy}$ (assuming $y\geq0$ for the square root to be real in the context of simplification). So, $3\sqrt{xy^3}=3y\sqrt{xy}$ and $8\sqrt{xy^3}=8y\sqrt{xy}$.

Step2: Combine like terms

Now we have $3y\sqrt{xy}+8y\sqrt{xy}$. Since the terms have the same radical part ($y\sqrt{xy}$), we can combine the coefficients: $(3y + 8y)\sqrt{xy}=11y\sqrt{xy}$.

Answer:

$11y\sqrt{xy}$