Question

select the correct answer.

what is this expression in simplified form?

(12sqrt{2} - sqrt{18})

• (-11sqrt{16})
• (12sqrt{2} - 9)
• (9sqrt{2})
• (sqrt{6})

Explanation:

⚡ Using what you learned: simplifying radical expressions

Step 1: Simplify the radical term

$$ \sqrt{18} = \sqrt{9 \cdot 2} = \sqrt{9} \cdot \sqrt{2} = 3\sqrt{2} $$

Step 2: Subtract like terms

$$ 12\sqrt{2} - 3\sqrt{2} = (12 - 3)\sqrt{2} = 9\sqrt{2} $$

Answer:

\( 9\sqrt{2} \) (the third option)