### Instruction: Simplify: $\sqrt{50} + \sqrt{18}$ . Express your answer in simplest radical form.### Response: To simplify a sum of two square roots, I need to look for perfect square factors inside the radicands (the numbers under the square root sign).
For $\sqrt{50}$, I can rewrite it as $\sqrt{25 \cdot 2}$, since 25 is a perfect square factor of 50.
Similarly, for $\sqrt{18}$, I can rewrite it as $\sqrt{9 \cdot 2}$, since 9 is a perfect square factor of 18.
Now, using the property that $\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}$, I can split the square roots of the products into products of the square roots of the factors.
This gives me: $\sqrt{50} + \sqrt{18} = \sqrt{25 \cdot 2} + \sqrt{9 \cdot 2} = \sqrt{25} \cdot \sqrt{2} + \sqrt{9} \cdot \sqrt{2}$.
Next, I can simplify the square roots of the perfect squares, since I know their exact values.
This gives me: $\sqrt{25} \cdot \sqrt{2} + \sqrt{9} \cdot \sqrt{2} = 5 \cdot \sqrt{2} + 3 \cdot \sqrt{2}$.
Finally, I can combine the like terms, since they have the same radical part.
I just need to add the coefficients in front of the $\sqrt{2}$.
This gives me: $5 \cdot \sqrt{2} + 3 \cdot \sqrt{2} = (5 + 3) \cdot \sqrt{2} = 8 \cdot \sqrt{2}$.