\begin{tabular}{l} Add or subtract the radical expressions, if possible. \ Select "Cannot be simplified" if applicable. \ $$ \qquad 10 \sqrt{p}+4 \sqrt{q}-6 \sqrt{p}=\square $$ \ $$ \begin{array}{l} ext { Cannot } \ ext { be } \ ext { simpified }\end{array} $$ \ \hline\end{tabular}

Question

\begin{tabular}{l} Add or subtract the radical expressions, if possible. \ Select "Cannot be simplified" if applicable. \ $$ \qquad 10 \sqrt{p}+4 \sqrt{q}-6 \sqrt{p}=\square $$ \ $$ \begin{array}{l}	ext { Cannot } \ 	ext { be } \ 	ext { simpified }\end{array} $$ \ \hline\end{tabular}

UpStudy AI · Accepted Answer

To simplify the expression $$ 10 \sqrt{p} + 4 \sqrt{q} - 6 \sqrt{p} $$, follow these steps:

1. **Combine Like Terms:**
   
   - **Terms with $$\sqrt{p}$$:**
     $$
     10 \sqrt{p} - 6 \sqrt{p} = (10 - 6) \sqrt{p} = 4 \sqrt{p}
     $$
   
   - **Term with $$\sqrt{q}$$:**
     $$
     4 \sqrt{q} \quad \text{(remains unchanged)}
     $$

2. **Write the Simplified Expression:**
   $$
   4 \sqrt{p} + 4 \sqrt{q}
   $$

**Final Answer:**
$$
10 \sqrt{p} + 4 \sqrt{q} - 6 \sqrt{p} = 4 \sqrt{p} + 4 \sqrt{q}
$$

Since the radicals $$\sqrt{p}$$ and $$\sqrt{q}$$ have different radicands (i.e., $$p \neq q$$), the expression cannot be simplified further by combining these terms.
$$ 4 \sqrt{p} + 4 \sqrt{q} $$

\begin{tabular}{l} Add or subtract the radical expressions, if possible. \\ Select "Cannot be simplified" if applicable. \\ \( \qquad 10 \sqrt{p}+4 \sqrt{q}-6 \sqrt{p}=\square \) \\ \( \begin{array}{l}\text { Cannot } \\ \text { be } \\ \text { simpified }\end{array} \) \\ \hline\end{tabular}

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