Simplify \( \sqrt{50} + \sqrt{18} \).

To simplify the expression ( \sqrt{50} + \sqrt{18} ), we start by breaking down each square root into its prime factors:

1. For ( \sqrt{50} ):

• ( 50 = 25 \times 2 )

• Therefore, ( \sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \cdot \sqrt{2} = 5\sqrt{2} ).

2. For ( \sqrt{18} ):

• ( 18 = 9 \times 2 )

• Thus, ( \sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \cdot \sqrt{2} = 3\sqrt{2} ).

Now, we can combine the two simplified square roots:

[

\sqrt{50} + \sqrt{18} = 5\sqrt{2} + 3\sqrt{2} = (5 + 3)\sqrt{2} = 8\sqrt{2}.

]

This leads us to conclude that the final simplified expression is ( 8\sqrt{2} \