Question

Simplify the expression by combining the radical terms using the indicated operations(s) Assume all variables are positive.

Answer 1

`38x\sqrt[]{34xy}`

Explanation:

Given the below expression;

`8x\sqrt[]{34xy}+3x\sqrt[]{34xy}+9x\sqrt[]{306xy}`

We'll go ahead and simplify the given expression following the below steps;

Step 1: Combine like terms;

`\begin{gathered} (8x\sqrt[]{34xy}+3x\sqrt[]{34xy})+9x\sqrt[]{306xy} \\ 11x\sqrt[]{34xy}+9x\sqrt[]{306xy} \end{gathered}`

Step 2: Split the radicand of the second term as seen below;

`\begin{gathered} 11x\sqrt[]{34xy}+9x\sqrt[]{9\cdot34\cdot xy} \\ =11x\sqrt[]{34xy}+9x(\sqrt[]{9}\cdot\sqrt[]{34xy}) \\ =11x\sqrt[]{34xy}+9x\cdot3\sqrt[]{34xy} \\ =11x\sqrt[]{34xy}+27x\sqrt[]{34xy} \end{gathered}`

Step 3: Combine like terms;

`\begin{gathered} 11x\sqrt[]{34xy}+27x\sqrt[]{34xy} \\ =38x\sqrt[]{34xy} \end{gathered}`