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

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

• A. 6
• B. 8
• C. \( 8\sqrt{2} \)
• D. \( 3\sqrt{2} + 5\sqrt{2} \)

Answer: (C)

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} \

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} \